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)`
C. `(a_(x)-a_(y))/(sqrt(2))`
D. `a_(x) + a_(y) + a_(z)`

Answer

C

Explanation

Component of `vecA` along `(hati - hatj)`is
`vecA .hatn =(a_(x) hati + a_(y)hatj+ a_(z)hatk).((hati-hatj)/(sqrt(2)))- (a_(x)- a_(y))/(sqrt(2))`