Supplementary Exercise Q7

Transcript

Supplementary Exercise Q7 Show that the four points A, B, C and D with position vectors 4 + 5 + , ( + ), 3 + 9 + 4 and 4 + 4 + 4 , respectively are co-planar Four points A, B, C, D are coplanar if the three vectors , and are coplanar. i.e. , , = 0 , , = 4 6 2 1 4 3 8 1 3 = 4 4 3 ( 1 3) ( 6) 1 3 ( 8 3) + ( 2) 1 1 ( 8 4) = 4 12+3 +6 3+24 2 1+32 = 4 (15) + 6 (21) 2 (33) = 60 + 126 66 = 126+ 126 = 0 , , = 0 Therefore, points A, B, C and D are coplanar.