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Test: Resolution of Vectors (NCERT)


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Test: Resolution of Vectors (NCERT) - Question 1

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

Detailed Solution for Test: Resolution of Vectors (NCERT) - Question 1

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 (NCERT) - Question 2

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

Detailed Solution for Test: Resolution of Vectors (NCERT) - Question 2

Given , (say) components of along the direction of

Test: Resolution of Vectors (NCERT) - Question 3

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 (NCERT) - Question 3


Squaring both sides we get 

Test: Resolution of Vectors (NCERT) - Question 4

The direction cosines ofare 

Detailed Solution for Test: Resolution of Vectors (NCERT) - Question 4

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

Test: Resolution of Vectors (NCERT) - Question 5

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 (NCERT) - Question 5

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

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