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.

Find the angle between force F= (3hati+4hatj-5hatk) unit and displacem

1.	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.
Answer» Solution :`Fd = F_(x)d_(x)+F_(y)d_(y)+F_(Z)d_(z)` `=3(5)+4(4)+(-5)(3)= 16` unit. Hence `Fd= Fd cos THETA= 16` unit Now `FF= F^(2)= F_(x)^(2)+F_(y)^(2)+F_(z)^(2)` `=9+1625= 50` unit and `dd= 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`.