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Vector vec(A) makes equal angles with x-...

Vector `vec(A)` makes equal angles with x-,y-,and z-axis. Find the value of its components (in terms of magnitude of `vec(A)`)

A

`A/(sqrt(3))`

B

`A/(sqrt(2))`

C

`sqrt(3)A`

D

`(sqrt(3))/A`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the components of `vec(A)` makes angles `alpha, beta and gamma` with x,y and z axis respectively then `alpha=beta=gamma`
`cos^(2)theta+cos^(2)beta+cos^(2)gamma=1`
`implies 3 cos^(2)theta=1implies cos alpha= 1/(sqrt(3))`
`:. A_(x)=A_(y)=A_(z)= A cos alpha= (A)/(sqrt(3)`
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