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Scalar Triple Product

If a⃗ and b⃗ ...

Question

$If \to a and \to b$ are mutually perpendicular unit vectors, then $(3 \to a + 2 \to b) \cdot (5 \to a - 6 \to b) =$

A

5

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B

3

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C

6

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D

12

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Solution

The correct option is B $3$
$\to a and \to b$ are perpendicular.
$\Rightarrow \to a \cdot \to b = \to b \cdot \to a = 0$
$Also, | \to a | = | \to b | = 1$
$Now, (3 \to a + 2 \to b) \cdot (5 \to a - 6 \to b)$
$= 3 \to a \cdot (5 \to a - 6 \to b) + 2 \to b (5 \to a - 6 \to b)$
$= 15 | \to a |^{2} - 18 \to a \cdot \to b + 10 \to b \cdot \to a - 12 | \to b |^{2}$
$= 15 - 12 = 3$

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