What is the angle between two vectors `vec P =2hati +3hatj +hatk and vec Q =-3hati +6hatk`.

Options

A. `0^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

Let `vec P =2hati + 3hatj + hatk and vec Q =-3hati +6hatk`
The angle `(theta)` between the two vectors is given by
`cos theta =(vec P cdot vec Q)/(|P| |Q|)`
`cos theta =((2hati +3hatj + hatk) cdot (-3hati +6hatk))/(sqrt(2^(2)+3^(2)+1)sqrt((-3)^(2) + (6)^(2)))`
`=((2xx-3) + 3xx0+6xx1)/(sqrt(14)sqrt(45))`
`=(-6 +6)/(sqrt(14)sqrt(45))=0`
`because cos theta =0" "therefore theta =90^(@)`