The three points A, B, C with position vectors $- 2 a + 3 b + 5 c, a + 2 b + 3 c, 7 a - c$

Coinitial

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Colinear

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equal

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None of these

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Solution

The correct option is B Colinear
Let O be the origin of reference.
We have
$\to A B = \to O B - \to O A = (a + 2 b + 3 c) - (- 2 a + 3 b + 5 c) = 3 a - b - 2 c$
$\to A C = \to O C - \to O A = (7 a - c) - (- 2 a + 3 b + 5 c) = 9 a - 3 b - 6 c = 3 \to A B$
Thus the vectors $\to A B$ and $\to A C$ are collinear. These vectors being also coterminous, the points A, B and C are collinear.

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Similar questions

- 2 a + 3 b + 5 c, a + 2 b + 3 c

7 a - c

7 \to a - \to c

\to a + 2 \to b + 3 \to c

- 2 \to a + 3 \to b + 5 \to c

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