Mathematics Part-II

Book: Mathematics Part-II

Chapter: 10. Vector Algebra

Subject: Maths - Class 12th

Q. No. 8 of Miscellaneous Exercise

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8

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.


8

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If , then is it true that ? Justify your answer.