If the point(-1, -1, 2), (2, m, 5) and (3, 11,6) are collinear find the value of m.
Answers
We have to find the value of m if (-1, -1, 2) , (2, m, 5) and (3, 11, 6) are collinear.
Solution : we know, three points A,B and C are collinear only if direction ratios of them would be AB and BC are proportional.
direction ratio of AB = B - A
= (2, m, 5) - (-1, -1, 2)
= (3, m + 1, 3)
direction ratio of BC = C - A
= (3, 11, 6) - (2, m, 5)
= (1, 11 - m , 1)
Now ratio of them,
3/1 = (m + 1)/(11 - m) = 3/1
⇒(m + 1)/(11 - m) = 3
⇒m + 1 = 33 - 3m
⇒4m = 32
⇒m = 8
therefore the value of m is 8 if given points are collinear.
Answer:-
We have to find the value of m if (-1, -1, 2) , (2, m, 5) and (3, 11, 6) are collinear.
Solution :
we know, three points A,B and C are collinear only if direction ratios of them would be AB and BC are proportional.
direction ratio of AB = B - A
= (2, m, 5) - (-1, -1, 2)
= (3, m + 1, 3)
direction ratio of BC = C - A
= (3, 11, 6) - (2, m, 5)
= (1, 11 - m , 1)
Now ratio of them,
3/1 = (m + 1)/(11 - m) = 3/1
⇒(m + 1)/(11 - m) = 3
⇒m + 1 = 33 - 3m
⇒4m = 32
⇒m = 8
therefore the value of m is 8 if given points are collinear.
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