Question:
4. If the points A ( 1, 0 , -6 ), B ( -3, p, q ) and C ( -5, 9, 6) are collinear, find the values of p and q
Answer:
If 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.
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