The angles between the two vectors `vecA=3hati+4hatj+5hatk` and `vecB=3hati+4hatj-5hatk` will be

Options

A. `180^(@)`
B. `45^(@)`
C. `90^(@)`
D. `0^(@)`

Answer

C

Explanation

The angle between the two vector `vec A and vec B` is given by
`cos theta =(vec A cdot vec B)/(AB)`
In this case `vec A = 3hati + 4hatj +5hatk`
`therefore A = sqrt (3^(2)+4^(2) +5^(2))=sqrt(50) and vec B =3hati + 4 hatj -5hatk`
`therefore B = sqrt (3^(2) +4^(2) +5^(2)) =sqrt(50) and vec A cdot vec B =(3hati +4hatj +5hatk) cdot (3hati + 4hatj -5hatk)`
`=9+16-25=0`
`therefore cos theta =(0)/(sqrt(50)-sqrt(50))=0`
`therefore theta =90^(@)`