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Applications of Dot Product

If vector a...

Question

If vector $\to a = 2^i - 3^j + 6^k$ and vector $\to b = - 2^i + 2^j -^k$ , then ratio of Projection of $\to a$ on vector $\to b$ to Projection of $\to b$ on $\to a$ is equal to

A

\frac{3}{7}

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B

\frac{7}{3}

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C

3

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D

7

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Solution

The correct option is C $\frac{7}{3}$
From the condition given we get

$= \frac{\frac{a . b}{| b |}}{\frac{b . a}{| a |}}$
Now we know that $a . b = b . a$ ...(by property of scalar/dot product of vectors).
Hence the above expression simplifies as
$\frac{| a |}{| b |}$

$= \frac{7}{3}$

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