DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

NEET: DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

The document DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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Q31. Which one is a vector quantity?
(a) Time
(b) Temperature
(c) Flux density
(d) Magnetic field intensity

Magnetic field intensity.
Option (d) is correct.Vector Quantity has both Magnitude and DirectionVector Quantity has both Magnitude and Direction


Q32. Given that P = 12,Q = 5 and R =13 also DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET then the angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET will be
(a) π 
(b) π/2
(c) zero
(d) π/4

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
∴ Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (b) is correct.


Q33. The forces, which meet at one point but their lines of action do not lie in one plane, are called 
(a) non-coplanar non-concurrent forces 
(b) non-coplanar concurrent forces 
(c) coplanar concurrent forces 
(d) coplanar non-concurrent forces

non-coplanar concurrent forces


Q34. Given that DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET Two out of the three vectors are equal in magnitude. The magnitude of the third vector is √2 times that of the other two. Which of the following can be the angles between these vectors? 
(a) 90°, 135°, 135° 
(b) 45°, 45°, 90° 
(c) 30°, 60°, 90° 
(d) 45°, 90°, 135°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET …(i) 
Let Q2 = P2 and R = P√2
Thus, Eq. (i) takes the form
P2 + P2 + 2PQcos θ = 2P2 
or 2PQcos θ = 0
or cosθ = 0
or  θ = 90°
∴ Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or P2 + R2 + 2PR cos φ = Q2
or 2PR cos φ = Q2 - P2 - R2
or   2PR cos φ = - R2
or   2P cos φ = - R
or    2P cos φ = - P√2
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
∴ φ = 135°

∴  Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (a) is correct.


Q35. The angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(a) 90° 

(b) between 0° and 180°
(c) 180° only
(d) None of these

Angle (φ) between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Angle φ between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
This implies that angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET and DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET will vary from 0 to π.
Option (b) is correct.


Q36. Two vectors of equal magnitude have a resultant equal to either of them, then the angle between them will be 
(a) 30° 
(b) 120° 
(c) 60° 
(d) 45°

R2 = P2 + Q2 + 2PQcosθ
for R = P = Q
P2 = P2 + P2 + 2PPcos θ
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or    θ = 120°
Option (b) is correct.


Q37. A forceDC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET newton acts on a body and displaces it by DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEETmetre. The work done by the force is 
(a) 5 J 
(b) 25 J 
(c) 10 J 
(d) 30 J

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
= 25 J
Option (b) is correct.


Q38. If the vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET are perpendicular to each other then the positive value of a is 
(a) zero 
(b) 1 
(c) 2 
(d) 3

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Other value is - ive.
Option (d) is correct.


Q39. The angles which the vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET makes with the co-ordinate axes are
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(d) none of the above

If a vector makes angles α, β and γ with the co-ordinate axes, then
cos2 α + cos2 β + cos2 γ = 1
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
∴ Option (a) is correct.


Q40. Unit vector parallel to the resultant of vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(d) None of these

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET and DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (b) is correct.


Q41. The value of n so that vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET may be coplanar, will be 
(a) 18 
(b) 28 
(c) 9 
(d) 36

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
∴ Vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET will be coplanar if their scalar triple product is zero i.e.,

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or 65 - 4n + 7 = 0
or  n = 18
Option (a) is correct.


Q42. Which one of the following statement is false? 
(a) A vector has only magnitude, whereas a scalar has both magnitude and direction 
(b) Distance is a scalar quantity but displacement is a vector quantity 
(c) Momentum, force, torque are vector quantities 
(d) Mass, speed and energy are scalar quantities

A vector has only magnitude, whereas a scalar has both magnitude and direction


Q43.DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET are two vectors then the value of DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (a) is correct.


Q44. The angle between the two vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(a) 60° 
(b) 0° 
(c) 90° 
(d) None of these

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
= 0
⇒ θ = 90°
Option (c) is correct.


Q45. Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N respectively. The smaller force will be equal to 
(a) 5 N 
(b) 4 N 
(c) 2 N 
(d) 1 N

A + B = 7
A - B = 3
∴ B = 2 N
Option (c) is correct.


Q46. The component of vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET along the vectorDC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(a) 5/√2
(b) 10/√2
(c) 5 √2
(d) 5

Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
and  DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Component of  DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (a) is correct.


Q47. The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is 
(a) 60° 
(b) 120° 
(c) 70° 
(d) 180°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (b) is correct.


Q48. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is 
(a) 120° 
(b) 60° 
(c) 90° 
(d) 150°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
As   θ = 90°, tan α = ∞
∴ P + Q cos α  = 0
i.e., DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
∴ α = 120°
Option (a) is correct.


Q49. Three vectors satisfy the relation DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is parallel to
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET …(i)
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET …(ii)
From Eq. (i) and Eq. (ii), we conclude that DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is perpendicular to the plane containing 

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
This implies that DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is perpendicular to DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (c) is correct.


Q50. The sum of two forces at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N. Then two forces are 
(a) 6N, 10N 
(b) 8 N, 8 N 
(c) 4 N, 12N 
(d) 2 N, 14N

P2 + Q2 + 2PQ cos α = R2 
or P2 + Q2 + 2PQ cos α = 82
or P2 + Q2 + 2PQ + 2PQ cos α - 2PQ = 64
or (P + Q)2 + 2 PQ (cos α - 1) = 64
or   (16)2 + 2 PQ (cos α - 1) = 64
or   2 PQ (cos α - 1) = - 192
or   PQ cos α - PQ = - 96 …(i)

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(as θ = 90°)
∴ P + Q cos α = 0
Qcos α = -P …(ii)
Using Eq. (ii) and Eq. (i),
P (- P) - PQ = - 96

or - P (P + Q) = - 96
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
P = + 6 N
∴ Q = 10 N
Option (a) is correct.


Q51.DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET then the value of DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(a) (A2 + B2 + AB)1/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(c) (A + B)
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
⇒ tan θ = √3
⇒ θ = 60°
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
= A2 + B2 + 2AB cos 60°
= A2 + B2 + AB
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET


Q52. If the angle between the vectorsDC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET the value of the product DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEETis equal to
(a) BA2 cos θ
(b) BA2 sin θ
(c) BA2 sin θ cos θ
(d) zero

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is perpendicular to both DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (d) is correct.


Q53. If a vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is perpendicular to the vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET then the value of α is
(a) -1 
(b) 1/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
(d) 1

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
⇒ - 8 + 12 + 8a = 0
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (c) is correct.


Q54. Minimum number of vectors of unequal magnitudes which can give zero resultant are 
(a) two 
(b) three 
(c) four 
(d) more than four

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET


Q55. The (x, y, z) coordinates of two points A and B are given respectively as (0, 3, - 1) and (- 2, 6, 4). The displacement vector from A to B is given by
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Option (c) is correct.


Q56. The sum of two vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET is at right angles to their difference. Then 
(a) A = B 
(b) A = 2B
(c) B = 2A
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET have the same direction

Using answer to questions no. 35, as angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
A2 + B2 cos 2θ = 0
or  A2 = - B2 cos 2θ
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or  A2 = - B2 cos π
or   A2 = B2
⇒ A = B
Option (a) is correct.


Match the Columns

Q1. Column-I shows some vector equations. Match column I with the value of the angle between A and B given in column II.

Column IColumn II
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET(p) zero
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET(q) π/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET(r) π/4
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET(s) 3π/4

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
Thus, (a) → (r) (s).

DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET (given)
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or sin θ = - sin θ
or   2 sin θ = 0
⇒ θ = 0 rad
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or  DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Units, Dimensions & Vectors - 2 Notes | Study Physics Class 11 - NEET

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