Question

If the points a(1,0,-6), b(-5,9,6) and c(-3,p,q) are collinear, find the value of p and q

Answer 1

The solution is attached as a word file

5b637a01b9637f0d305eeb0d82b7b9ed.doc

Answer 2

The value of p and q is 6 and 2 respectively.

• To check the whether the points are collinear we check the direction ratios of AB, BC and CA.
• If the points are collinear then the direction ratios of AB,BC and CA will be proportional.
• So, we calculate the direction ratios of AB = (-5-1,9-0,6-(-6)) = (-6,9,12)
• Direction ratios of BC = (-3+5,p-9,q-6) = (2,p-9,q-6)
• Direction ratios of CA = (1+3,0-p,-6-q) = (4,-p,-6-q)
• Now we take the ratios of the direction ratios as the points are collinear the direction ratios are proportional.

4/-6 = -p/9 = -6-q/12

We take,

4/-6 = -p/9

p = 6

• Now we find the value of q

4/-6 = -6-q/12

6+q = 8

q =2