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

Explanation

Hint `vecF.vecd = F_(x)d_(x)+F_(y)d_(y)+F_(z)d_(z)`
`vecF.vecF=F_(x)^(2)+F_(y)^(2)+F_(z)^(2)+F_(z)^(2)" "vecd.vecd=d^(2)=d_(x)^(2)+d_(y)^(2)+d_(z)^(2)`
`cos theta=(vecF.vecd)/(Fd)" Projection of "vecF" on " vecd=F cos theta`
`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 "vecF" on "vecd=F cos theta=5xx0.48=2.4`