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

Explanation

`vecFvecd=F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)`
`vecFvecF=F^(2)=F_(x)^(2)+F_(y)^(2)+F_(z)^(2)" "vecdvecd=d^(2)=d_(x)^(2)=d_(y)^(2)+d_(z)^(2)`
`cot theta(vecFvecd)/(Fd)"Projection of "vecFon vecd=F costheta`
`vecF.vecd=F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)`
`=4(0)+3(4)+0(-3)=12` unit
`vecF.vecF=F^(2)=F_(x)^(2)+F_(y)^(2)+F_(z)^(2)=4^(2)+3^(2)=25`
`vecd.vecd=d^(2)=d_(x)^(2)+d_(y)^(2)+d_(z)^(2)=4^(2)+(-3)^(2)=25`
`cos theta=(vecF.vecd)/(Fd)=(12)/(5xx5)=0.48`
`theta=cos^(-1)(0.48)`
projection of `vecFon vecd=Fcostheta=5xx0.48=2.4`