If there are two vectors `vec(A)` and `vec(B)` such that `vec(A)+vec(B)=hat(i)+2hat(j)+hat(k)` and `vec(A)-vec(B)=(hat(i)-vec(k))`, then choose the correct options.

Options

A. the angle between `vec(A)` and `vec(B)` is `60^(@)`
B. `vec(A) = hat(i) + hat(j)`
C. `vec(B) = hat(j) + hat(k)`
D. the angle between `vec(A)` and `vec(B)` is `120^(@)`

Answer

A, B, C

Explanation

`2overset(vec)(A) = 2hat(i) + 2hat(j)`
`2overset(vec)(B) = 2hat(j) + 2hat(k)`
`overset(vec)(A) = hat(i) + hat(j), overset(vec)(B) = hat(j) + hat(k)`
`cos theta = (overset(vec)(A).overset(vec)(B))/(AB) rArr cos theta = (1)/(2) rArr theta = 60^(@)`