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Test for Collinearity of Vectors

If vectors ...

Question

If vectors $a ¯ i + a ¯ j + c ¯ ¯ ¯ k, ¯ i + ¯ ¯ ¯ k, c ¯ i + c ¯ j + b ¯ ¯ ¯ k$ are coplanar, then $C$ is

A

A.M of

a, b

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B

G.M of

a, b

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C

H.M of

a, b

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D

0

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Solution

The correct option is A G.M of $a, b$
$a^i + a^j + c^k = λ (^i +^k) + μ (c^i + c^j + b^k)$
$λ + c μ = a$ -----(1)
$c μ = a$ -----(2)
$λ = 0; c = μ b$ ---------(3)
$μ = \frac{a}{c};$ $c^{2} = a b$

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