The component of vector `A=a_(x)hati+a_(y)hatj+a_(z)hatk` and the directioin of `hati-hatj` is

Options

A. `A_(x)-A_(y) +A_(z)`
B. `A_(x)+A_(y)+A_(z)`
C. `A_(x)-A_(y)`
D. `(A_(x) -A_(y))/(sqrt(2))`

Answer

D

Explanation

Magnitude of vector `vec A`
`=|bar A|=sqrt(A_(x)^(2) + A_(y)^(2)+A_(z)^(2))` Where `A_(x), A_(y) and A_(z)` are the magnitudes of the projections of `vec A` along the co-ordinate axes X,Y, and Z respectively.
`therefore vec r - vec j = vec i+(-vecj)`
The magnitude is `sqrt(1^(2)+1^(2)) = sqrt(2)`
`therefore` Component of the vector `vec A =(A_(x) - A_(y))/(sqrt(2))`