# a level maths 3d vector cuboid two lines bisect

can someone help me answer this question?

The diagram shows a cuboid whose vertices are O, A, B, C, D, E, F and G. a, band c are the vectors OA , OB and OC respectively. The points M and N lie on OA such that OM MN NA : : 1: 2:1 ï€½. The points K and L lie on EF such that EK KL LF : : 1: 2:1 ï€½Figure 1Prove that the diagonals KN and ML bisect each other at P.
(edited 4 years ago)
Original post by dbgzhthtth
can someone help me answer this question?

The diagram shows a cuboid whose vertices are O, A, B, C, D, E, F and G. a, band c are the vectors OA , OB and OC respectively. The points M and N lie on OA such that OM MN NA : : 1: 2:1 ï€½. The points K and L lie on EF such that EK KL LF : : 1: 2:1 ï€½Figure 1Prove that the diagonals KN and ML bisect each other at P.

Work out the midpoint of KN, in terms of a,b,c.

Work out the midpoint of ML, in terms of a,b,c.

Recognize that these are the same (assuming you've done it correctly), and hence the two lines bisect each other at that point, which we'll call P.
i got 3 A* in alevels fyi