1.

The angle between `A=hat(i)+hat(j) " and " B=hat(i)-hat(j)` isA. `45^(@)`B. `90^(@)`C. `-45^(@)`D. `180^(@)`

Answer» Correct Answer - B
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^(@)`


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