Find the angle between force `F= (3hati+4hatj-5hatk)` unit and displacement `d= (5hati+4hatj+3hatk)` unit. Also find the projection of F and d.

Explanation

`F*d = F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)`
`=3(5)+4(4)+(-5)(3)= 16` unit.
Hence `F*d= Fd cos theta= 16` unit
Now `F*F= F^(2)= F_(x)^(2)+F_(y)^(2)+F_(z)^(2)`
`=9+1625= 50` unit
and `d*d= d^(2)= d_(x)^(2)+d_(y)^(2)+d_(z)^(2)`
`=25+16+9= 50` unit
`cos theta= (16)/(sqrt(50)sqrt(50))= (16)/(50)= 0.32`
`theta = cos^(-1) 0.32`.