The angle between `vecA = hati + hatj and vecB = hati - hatj` is

Options

A. `45^(@)`
B. `90^(@)`
C. `-45^(@)`
D. `180^(@)`

Answer

B

Explanation

Given : `vecA = hati + hatj, vecB = hati - hatj`
`therefore|vecA| = sqrt((1)^(2) + (1)^(2)) = sqrt(2) and |vecB| = sqrt((1)^(2) + (-1)^(2)) = sqrt(2)`
let `theta` be angle between the vectors `vecA and vecB`. Then according to definition of scalar product (or dot product)
`vecA *vecB = |vecA||vecB| costheta or cos theta = (vecA*vecB)/(|vecA||vecB|) = ((hati+hatj)*(hati-hatj))/((sqrt(2))(sqrt(2)))= 0`
`therefore theta = cos^(-1) (0) = 90^(@)`