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Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - NEET MCQ


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10 Questions MCQ Test - Test: Resolution of Vectors & Vector addition- Analytical Method (May 14)

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Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 1

The direction cosines ofare 

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 1

Let ∴ Ax = 1, Ay = 1, Az = 1
and
cos α, cos β andcos y are the direction cosines of .

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 2

Two vectors inclined at an angle θ have a resultantwhich makes an angle α  withand angle β  withLet the magnitudes of the vectors be represented by A, B and R respectively. Which of the following relations is not correct?

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 2

Let OP and OQ represent two vectorsmaking an angle (α + β). Using the parallelogram method of vector addition,
Resultant vector, 
SN is normal to OP and PM is normal to OS.
From the geometry of the figure,
OS2 = ON2 + SN2 = (OP + PN)2 + SN= (A + Bcos(α + β))+ (Bsin(α + β))2

R2 = A+ B+ 2ABcos(α + β)

In ΔOSN, SN = OSsinα = Rsinα and in ΔPSN,SN = PSsin(α + β) = Bsin(α + β)
Rsinα = Bsin(α + β) or R/sin(α + β)= B/sinα
Similarly,
PM = Asinα = Bsinβ
A/sinβ = B/sinα
Combining (i) and (ii), we get
R/sin(α + β) = A/sinβ = B/sinα
From eqn, (iii), Rsinβ = Asin(α + β)

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Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 3

If n is a unit vector in the direction of the vector then

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 3

Unit vector is vector with magnitude unity but having specific direction.

Value of unit vector is given by:

Where,

 = unit vector

A = vector a

∣A∣ = magnitude of vector a

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 4

Vectorsinclude an angle θ between them. Ifrespectively subtend angles α and β with then (tanα + tanβ) is :

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 4

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 5

Which of the following quantities is dependent of the choice of orientation of the coordinate axes?

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 5

A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes. So angle between are independent of the orientation of the coordinate axes. But the quantity Ax + Bdepends upon the magnitude of the components along x and y axes, so it will change with change in coordinate axes.

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 6

The components of Vector ​ along the directions of vectors () is

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 6

Given , (say) components of along the direction of

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 7

A unit vector perpendicular to i^−2j^​+k^ and 3i^−j^​+2k^ is

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 7

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 8

The magnitude of the x-component of vector is 3 and the magnitude of vector is 5. What is the magnitude of the y-component of vector ?

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 8


Squaring both sides we get 

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 9

If a vector makes angles α, β and γ  with X, Y and Z axes respectively then sin2α + sin2β + sin2γ is equal to 

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 9

cos2 α + cos2 β + cos2 Y = 1
(1 - sin2 α) + (1 - sin2 β) + (1 - sinY) = 1
or sin2 α + sin2 β + sin2 Y = 3 - 1 = 2

Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 10

A unit vector in the direction of resultant vector of 

Detailed Solution for Test: Resolution of Vectors & Vector addition- Analytical Method (May 14) - Question 10

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