A vector `vec A` is exparessed as ` vec A = A_(x) hat I + A_(y) hat j` where ` vec A and vec B` are its components along x-axis and y-axis respectively. If vector `vec A` makes an angle `theta` with x-axis, then `theta` is given by which expressinon ?

Options

A. `A_(x)= B_(x), A_(y)= - B_(y), A_(z)= - B_(z)`
B. `A_(x)= B_(x), A_(y)= B_(y), A_(z)= - B_(z)`
C. `A_(x)= B_(x), A_(y)= B_(y), A_(z)= B_(z)`
D. `A_(x)= - B_(x), A_(y)= - B_(y), A_(z)= - B_(z)`

Answer

D

Explanation

`vec(A) = A_(x) hat(i) + A_(y) hat(j) + A_(z) hat(k) and vec(B) = B_(x) hat(i) + B_(y) hat(j) + B_(z) hat(k)`
`vec(A) + vec(B) = 0 rArr (A_(x) + B_(x)) hat(i) + (A_(y) + B_(y)) hat(j) + (B_(z) + A_(z)) hat(k)= 0`
`rArr A_(x) + B_(x)= 0 rArr A_(x)= - B_(x)`
`A_(y) + B_(y)= 0 rArr A_(y)= - B_(y)`
`A_(z) + B_(z)= 0 rArr A_(z)= - B_(z)`