If the projections of the line segment AB¯ on the yz-plane, zx-plane, xy- plane are  160,153  and  5 respectively, then the projection of AB¯on the z-axis is

The projection of the line segment AB¯ on the yz-plane is  y2−y12+z2−z12=160The projection of the line segment AB¯on the zx-plane is  z2−z12+x2−x12=153The projection of the line segment AB¯on the xy-plane is x2−x12+y2−y12=5It implies that x2−x12+y2−y12+z2−z12=169Hence,z2−z12=169−25=144Apply square root on both sidesz2−z1=12 , this is the length of the projection ofAB¯  on z- axis.