Which of th efollowing is/are correct regarding vectors `vec(A) = 2hat(i) + hat(j)` and `vec(B) = 2hat(i) - 4 hat(j)`.

Options

A. Angle between `vec(A)` and `vec(B)` is acute
B. Angle between `vec(A) + vec(B)` and `vec(A)` is acute
C. `hat(k)` is a unit vector perpendicular to `vec(A)`
D. `(hat(i) - 2 hat(j))/(sqrt5)` is a unit vector perpendicular to `vec(A)`

Answer

B, C, D

Explanation

(A) `vec(A).vec(B) = AB cos theta = 0`
`rArr theta = 90^(@)`
Angle between `vec(A)` & `vec(B)` in `90^(@)`
(B) `vec(A) + vec(B) = 4 hat(i) - 3 hat(j)`
`(vec(A) + vec(B)).vec(A) = 8 - 3`
`= 5 (+ve)`
So, angle between `vec(A) + vec(B)` & `vec(A)` in acute
(C ) z-axis is perpendicular to `x - y` plae
`|(hat(i) - 2 hat(j))/(sqrt5)| = 1`
`(2 hat(i) + hat(j)).((hat(i) - 2 hat(j))/(sqrt5)) = 0`