If  A1,2,3,B2,3,4,C3,4,5,D4,5,6are four points, then the projection of BD¯  on  AC¯  is

The projection of BD¯  on  AC¯ isBD¯ ⋅ AC¯AC¯Hence, BD¯ ⋅ AC¯AC¯=OB¯−OD¯⋅OC¯−OA¯OC¯−OA¯=2i+3j+4k−4i+5j+6k⋅3i+4j+5k−i+2j+3k3i+4j+5k−i+2j+3k=−2i−2j−2k⋅2i+2j+2k4+4+4=1212Therefore, the required projection is  23