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

Explanation

`vecFvecd=F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)`
`vecF.vecF=F^(2)=F_(x)^(2)+F_(z)^(2)" "vecd.vecd=d_(x)^(2)+d_(y)^(2)+d_(z)^(2)`
`costheta(vecFvecd)/(Fd)`
Projecto of `vecF on vecd=Fcostheta`
`vecF.vecd=F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)=5(3)+4(4)+(-3)(5)=16` unit
`vecF.vecF=F^(2)+F_(x)^(2)+F_(y)^(2)+F_(z)^(2)=5^(2)+4^(2)+(-3)^(2)=50` unit
`vecd.vecd=d^(2)=d_(x)^(2)+d_(y)^(2)+d_(z)^(2)=3^(2)+4^(2)+5^(2)=50` unit
`cos theta=(vecF.vecd)/(Fd)=(16)/(sqrt50sqrt50)=0.32`
`theta=cos^(-1)(0.32)`
Projection of `vecFon vecd=F cos theta=sqrt50xx0.32=2.26`