Motion in a Plane Test

Result

Motion in a Plane Test - 4

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Weekly Quiz Competition

Question 1
4 / -1

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

A

B

C

D

Solution

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
Question 2
4 / -1

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

A
1/√2

B
- 1/√2

C
1/2

D
-1/2

Solution

Given , (say) components of along the direction of
Question 3
4 / -1

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 ?

A
3

B
4

C
5

D
8

Solution

Squaring both sides we get
Question 4
4 / -1

The direction cosines ofare

A
1, 1, 1

B
2, 2, 2

C
1/√2, 1/√2, 1/√2

D
1/√3, 1/√3, 1/√3

Solution

Let= ∴ A_x = 1, A_y = 1, A_z = 1
and
cos α, cos β andcos y are the direction cosines of .
Question 5
4 / -1

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

A
0

B
1

C
2

D
3

Solution

cos² α + cos² β + cos² Y = 1
(1 - sin² α) + (1 - sin² β) + (1 - sin²Y) = 1
or sin² α + sin² β + sin² Y = 3 - 1 = 2