Question

Formula must start with $ sign.

Answer 1

A = ( 1 , -1 , 3)

B = ( 2 , -4 , 5)

C = ( 5 , -13, 11)

If , all these points lie on the straight lines than ;-

=> AC = AB + BC

=> AB = √( 2-1 )² + ( -4 + 1)² +( 5-3 )²

=> AB = √ 1 + 9 + 4

=> AB = √ 14

=> AB = 2√5

=> BC = √ ( 5 - 2 )² + ( - 13 + 4 )² + ( 11 - 5 )²

=> BC = √ 9 + 81 + 36 = 3 √ 14

=> AC = √ ( 5 - 1 )² + ( - 13 + 1 )² + ( 11 - 3 )²

=> AC = √ 16 + 144 + 64

=> AC = 4 √ 14

=> AB + BC = AC

=> L. H. S = √ 14 + 3√ 14

=> L. H. S. = 4 √ 14 = AC

=> L. H. S. = R. H. S.

The given points are in a Straight line.