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# Unit & Dimensions Vectors(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

## DC Pandey (Questions & Solutions) of Physics: NEET

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## NEET : Unit & Dimensions Vectors(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

The document Unit & Dimensions Vectors(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev is a part of the NEET Course DC Pandey (Questions & Solutions) of Physics: NEET.
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Ques 31: Which one is a vector quantity?
(a) Time
(b) Temperature
(c) Flux density
(d) Magnetic field intensity

Sol: Magnetic field intensity.
Option (d) is correct.

Ques 32: Given that P = 12,Q = 5 and R =13 also  then the angle between  will be
(a) π
(b) π/2
(c) zero
(d) π/4
Ans: π/2
Sol:

∴ Angle between
Option (b) is correct.

Ques 33: 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
Ans: non-coplanar concurrent forces

Ques 34: Given that  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°
Ans: 90°, 135°, 135°
Sol:

or
or
or  …(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

or
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
∴ φ = 135°

∴  Angle between

Option (a) is correct.

Ques 35: The angle between
(a) 90°

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

Ans: between 0° and 180°
Sol: Angle (φ) between

Angle φ between

This implies that angle between  and  will vary from 0 to π.
Option (b) is correct

Ques 36: 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°
Ans: 120°
Sol: R2 = P2 + Q2 + 2PQcosθ
for R = P = Q
P2 = P2 + P2 + 2PPcos θ
or
or    θ = 120°
Option (b) is correct.

Ques 37: A force newton acts on a body and displaces it by metre. The work done by the force is
(a) 5 J
(b) 25 J
(c) 10 J
(d) 30 J
Ans: 25 J
Sol:

= 25 J
Option (b) is correct.

Ques 38: If the vectors  are perpendicular to each other then the positive value of a is
(a) zero
(b) 1
(c) 2
(d) 3
Ans: 3
Sol:

Other value is - ive.
Option (d) is correct.

Ques 39: The angles which the vector  makes with the co-ordinate axes are

(d) none of the above
Ans:
Sol: If a vector makes angles α, β and γ with the co-ordinate axes, then
cos2 α + cos2 β + cos2 γ = 1

∴ Option (a) is correct.

Ques 40: Unit vector parallel to the resultant of vectors

(d) None of these
Ans:
Sol:  and

Option (b) is correct.

Ques 41: The value of n so that vectors  may be coplanar, will be
(a) 18
(b) 28
(c) 9
(d) 36
Ans: 18
Sol:

∴ Vectors  will be coplanar if their scalar triple product is zero i.e.,

or 65 - 4n + 7 = 0
or  n = 18
Option (a) is correct.

Ques 42: 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
Ans: A vector has only magnitude, whereas a scalar has both magnitude and direction

Ques 43: are two vectors then the value of

Ans:
Sol:

Option (a) is correct.

Ques 44: The angle between the two vectors
(a) 60°
(b) 0°
(c) 90°
(d) None of these
Ans: 90°
Sol:

= 0
⇒ θ = 90°
Option (c) is correct.

Ques 45: 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
Ans: 2 N
Sol: A + B = 7
A - B = 3
∴ B = 2 N
Option (c) is correct.

Ques 46: The component of vector  along the vector
(a) 5/√2
(b) 10/√2
(c) 5 √2
(d) 5
Ans: 5/√2
Sol: Angle between
and

Component of

Option (a) is correct.

Ques 47: 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°
Ans: 120°
Sol:

Option (b) is correct.

Ques 48: 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°
Ans: 120°
Sol:

As   θ = 90°, tan α = ∞
∴ P + Q cos α  = 0
i.e.,

∴ α = 120°
Option (a) is correct.

Ques 49: Three vectors satisfy the relation  is parallel to

Ans:
Sol:

…(i)

…(ii)
From Eq. (i) and Eq. (ii), we conclude that  is perpendicular to the plane containing

This implies that  is perpendicular to
Option (c) is correct.

Ques 50: 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
Ans: 6N, 10N
Sol:  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)

(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
P = + 6 N
∴ Q = 10 N
Option (a) is correct.

Ques 51: then the value of
(a) (A2 + B2 + AB)1/2

(c) (A + B)

Sol:

⇒ tan θ = √3
⇒ θ = 60°

= A2 + B2 + 2AB cos 60°
= A2 + B2 + AB

Ques 52: If the angle between the vectors the value o f the product is equal to
(a) BA2 cos θ
(b) BA2 sin θ
(c) BA2 sin θ cos θ
(d) zero

Ans: zero
Sol: is perpendicular to both

or
Option (d) is correct.

Ques 53: If a vector  is perpendicular to the vector  then the value of α is
(a) -1
(b) 1/2

(d) 1
Ans:
Sol:
⇒ - 8 + 12 + 8a = 0

Option (c) is correct.

Ques 54: Minimum number of vectors of unequal magnitudes which can give zero resultant are
(a) two
(b) three
(c) four
(d) more than four
Sol:

Ques 55: The (x, y, z) co-ordinates 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

Ans:
Sol:

Option (c) is correct.

Ques 56: The sum of two vectors  is at right angles to their difference. Then
(a) A = B
(b) A = 2B
(c) B = 2A
have the same direction
Ans: A = B
Sol: Using answer to questions no. 35, as angle between
A2 + B2 cos 2θ = 0
or  A2 = - B2 cos 2θ
or
or  A2 = - B2 cos π
or   A2 = B2
⇒ A = B
Option (a) is correct.

Match the Columns

Ques 1: Column-I shows some vector equations. Match coloumn I with the value of angle between A and B given in column II.

 Column I Column II (p) zero (q) π/2 (r) π/4 (s) 3π/4

Sol:

or
or

Thus, (a) → (r) (s).

(given)
or
or
or sin θ = - sin θ
or   2 sin θ = 0

or

or

or
or
or
or

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