The angle between two vectors given by `(6hati+6hatk)` and `(7hati+4hatj+4hatk)` is:

Options

A. `cos ^(-1)((1)/sqrt(3))`
B. `cos^(-1)((5)/sqrt(3))`
C. `sin^(-1)((2)/sqrt(3))`
D. `sin^(-1)((sqrt(5))/(3))`

Answer

D

Explanation

`cos theta=(vecB.vecB)/(AB)=((6hati+6hatj-3hatk).(7hati+4hatj+4hatk))/((sqrt(6^(2)+6^(2)+3^(2)))(sqrt(7^(2)+4^(2)+4^(2))))`
`cos theta-(54)/(81)=(6)/(9)=(2)/(3)`
`sin theta=sqrt(1-cos^(2)theta)=sqrt(5)/(3)`