If a (1,2,3) b (2,3,4) c (p,q,6) are the collinear points find p and q?

Question

2693 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-01T04:03:50

#p=4, q=5#.

If #A(1,2,3), B(2,3,4) and C(p,q,6)# are collinear, then, the

vectors #vec(AB) and vec(AC)# must have same/opposite direction.

In the event, #EE" a "lambda in RR-{0}," such that, "vec(AC)=lambdavec(AB)#.

#:. (p,q,6)-(1,2,3)=lambda(2-1,3-2,4-3), lambda in RR-{0},#

# i.e., (p-1,q-2,3)=(lambda,lambda,lambda)#.

Consequently, #lambda=3 in RR-{0}, q=2+lambda=5, p=4#.

Thus, #p=4, q=5#, are the desired values!

Enjoy Maths.!