Question

Prove, by direction

cosines, that the points (1,2,3), (4,0,4) and (-2,4,2) are collinear ​

Answer 1

Answer:

Let P.V. of A = 1,2,3 =i+2j+3k

B= 4,0,4 =4i+0j+4k

C= -2,4,2 = -2i+4j+2k

P.V. of AB = (4i+0j+4k) - (i+2j+3k)

= 3i-2j+k

or p.v. of BC = (-2i+4j+2k) - (4i+0j+4k)

= -6i+4j-2k

or = -2(3i-2j+k)

p.v. of AB is equal to integral multiple of p.v. of BC . so given points are colliner