Book: Mathematics Part-II
Chapter: 10. Vector Algebra
Subject: Maths - Class 12th
Q. No. 8 of Miscellaneous Exercise
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Show that the points A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7) are collinear, and find the ratio in which B divides AC.
Given: A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7)
Then
Then
Thus the given points are collinear.
Now to find the ratio in which B divides AC. Let it be λ :1
On equating the terms, we get:
5(λ + 1) = 11λ + 1
⇒ 5λ + 5 = 11λ + 1
⇒ 4 = 6λ
⇒ λ = 4/6 = 2/3
Hence, B divides AC in the ratio 2:3.
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