If `hati,hatj` and `hatk` represent unit vectors along the x,y and z-axes respectively, then the angle `theta` between the vectors `(hati+hatj+hatk)` and `(hati+hatj)` is equal to :

Options

A. `sin ^(-1)((1)/sqrt(3))`
B. `sin^(-1)(sqrt((2)/(3)))`
C. `cos^(-1)((1)/sqrt(3))`
D. `90^(@)`

Answer

A

Explanation

`cos theta=(vecA.vecB)/(AB)=(1+1)/(sqrt3sqrt(2))=(2)/sqrt(6)=sqrt(2)/sqrt(3)`
`sin theta=sqrt(1-cos ^(2) theta)=(1)/sqrt(3)`
`theta=sin^(-1)((1)/sqrt(3))`