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Dot Product

If vector a i...

Question

If vector $\to a$ is collinear with vector $\to b = 3^i + 6^j + 6^k$ and $\to a \cdot \to b = 27.$ Then $\to a$ is equal to

A

^i + 2^j + 2^k

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B

2^i +^j +^k

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C

-^i - 2^j - 2^k

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D

2^i - 2^j + 2^k

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Solution

The correct option is A $^i + 2^j + 2^k$
Given, $\to a$ and $\to b$ are collinear.
Hence, $\to a = k \to b$
$\Rightarrow \to a \cdot \to b = 27 \Rightarrow k (\to b \cdot \to b) = 27, (∵ \to b = 3^i + 6^j + 6^k) \Rightarrow (9 + 36 + 36) k = 27 \Rightarrow k = \frac{1}{3}$
So, $\to a =^i + 2^j + 2^k$

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