The angle between force `vecF =(3hati+4hatj-5hatk)` unit and displacement `vecd = (5hati+4hatj+3hatk)` unit is

Options

A. `cos^(-1) (0.16)`
B. `cos^(-1) (0.32)`
C. `cos^(-1) (0.24)`
D. `cos^(-1) (0.64)`

Answer

B

Explanation

Here, `vecF=3hati+4hatj-5hatk` unit
`vecd=5hati+4hatj+3hatk` unit
`therefore |vecF|=sqrt((3)^2 +(4)^2 + (-5)^(2))=sqrt50` unit
`|vecd|=sqrt((5)^2+(4)^2+(3)^2)=sqrt50` unit
Let `theta` be angle between `vecF` and `vecd`
`therefore cos theta=(vecF.vecd)/(|vecF||vecd|)=((3hati+4hatj-5hatk).(5hati+4hatj+3hatk))/(sqrt50sqrt50)`
`=(15+16-15)/50=16/50 =0.32 "or" theta=cos^(-1) (0.32)`