Find the angle between force `F = (3 hat(i) + 4 hat(j) - 5 hat(k))` unit and displacement d ` = (5 hat(i) + 4 hat(j) + 3 hat(k))` unit. Also find the projection of F on d .

Explanation

F.d = `F_(x) d_(x) + F_(y)d_(y) + F_(z) d_(z) = 3(5) + 4(4) + (-5)`
(3) = 16 units
Hence, F.d `= F d cos theta = `16 units
Now `F.F = F^(2) - F_(x)^(2) + F_(y)^(2) + F_(z)^(2)`
= 9 + 16 + 25 = 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`