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Dot Product of Two Vectors

If p = 7 i ...

Question

If $p = 7 i - 2 i + 3 k$ and $q = 3 i + j + 5 k,$ then | p - 2 q | is equal to

4

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\sqrt{66}

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\sqrt{29}

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\sqrt{62} - 2 \sqrt{35}

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Solution

The correct option is D $\sqrt{66}$
We have,
$p = 7 i - 2 j + 3 k$
$q = 3 i + j + 5 k$

Therefore,
$p - 2 q = 7 i - 2 j + 3 k - 2 (3 i + j + 5 k)$
$p - 2 q = 7 i - 2 j + 3 k - 6 i - 2 j - 10 k$
$p - 2 q = i - 4 j - 7 k$

On taking mode, we get
$| p - 2 q | = \sqrt{1^{2} + (- 4)^{2} + (- 7)^{2}}$
$| p - 2 q | = \sqrt{1 + 16 + 49}$
$| p - 2 q | = \sqrt{66}$

Hence, this is the answer.

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