Question

If three points are collinear in 3d then find p and q

Answer 1

Answer:

Step-by-step explanation:

f the three points A, B and C are collinear, then the direction ration of AB is proportional to that of BC is proportional to that of CA

So, the direction ration of AB = (-3 - 1, p, q + 6) = (-4, p, q + 6)

The direction ration of BC = (-3 + 5, p - 9, q - 6) = (-2, p - 9, q - 6)

the direction ration of CA = (-5 - 1, 9 - 0, 6 + 6) = (-6, 9, 12)

Now, we have

-4/-6 = p/9 = (q + 6)/12

=> 4/6 = p/9

=> p/9 = 2/3

=> p = (2*9)/3

=> p = 2*3

=> p = 6  

and -4/-6 = (q + 6)/12

=>(q + 6)/12 = 4/6

=> q + 6 = (12*4)/6

=> q + 6 = 2*4

=> q + 6 = 8

=>  q = 8 - 6

=> q = 2

So, the value of p and q are 6 and 2 respectivelty.