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Test for Collinearity of Vectors

The points ...

Question

The points $2 ¯ a + 3 ¯ b + ¯ c, ¯ a + ¯ b, 6 ¯ a + 11 ¯ b + 5 ¯ c$ are

Collinear

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Coplanar but non collinear

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Non coplanar

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Cannot be detrmined

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Solution

The correct option is A Collinear
We have,
$- - \to A B = \to a + \to b - 2 \to a - 3 \to b - \to c = - \to a - 2 \to b - \to c$
$- - \to A C = 4 \to a + 8 \to b + 4 \to c \to A = 2 \to a + 3 \to b + \to c$
$- - \to A C = 4 (- \to a - 2 \to b - \to c) \to B = \to a + \to b$
$- - \to A C = - 4 - - \to A B \to C = 6 \to a + 11 \to b + 5 \to c$
Hence,
Option $A$ is correct answer.

Suggest Corrections

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