The angle between `A=hat(i)+hat(j) " and " B=hat(i)-hat(j)` is

Options

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

Answer

B

Explanation

Given, `A=hat(i)+hat(j)`
`B=hat(i)-hat(j)`
We know that
`A.B=|A||B|cos theta`
`rArr " " (hat(i)+hat(j)).(hat(i)-hat(j))=(sqrt(1+1))(sqrt(1+1)) cos theta`
where `theta` is the angle between A and B
`rArr " " cos theta=(1-0+0-1)/(sqrt(2)sqrt(2))=(0)/(2)=0`
`rArr " " theta=90^(@)`