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)`)

Options

A. `(A)/(sqrt3)`
B. `(A)/(sqrt2)`
C. `sqrt3A`
D. `(sqrt3)/(A)`

Answer

A

Explanation

If vector `vec(A)` makes equal angles `alpha, beta and gamma` with x, y and z respectively then `alpha= beta= gamma`
`cos^(2) alpha+ cos^(2) beta + cos^(2) gamma=1 rArr 3 cos^(2) alpha=1`
`rArr cos alpha= (1)/(sqrt3)`
`vec(A)= (A cos alpha) hat(i) + (A cos beta) hat(j) + (A cos gamma) hat(k)`
Component `A_(x)= A_(y)= A_(z)= A cos alpha= (A)/(sqrt3)`