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Cross Product of Two Vectors

If a,b=π6,c i...

Question

If $(\to a, \to b) = \frac{π}{6}, \to c$ is perpendicular to $\to a$ and $\to b, ∣ ∣ \to a ∣ ∣ = 3, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 4, ∣ ∣ \to c ∣ ∣ = 6,$ $then ∣ ∣ ∣ [\to a \to b \to c] ∣ ∣ ∣$ is equal to

A

12 \sqrt{3}

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B

48 \sqrt{3}

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C

36

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D

76

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Solution

The correct option is C $36$
Given: $∣ ∣ \to a ∣ ∣ = 3, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 4, ∣ ∣ \to c ∣ ∣ = 6$
$| [\to a \to b \to c] | = | [\to c \to a \to b] | = | \to c . (\to a \times \to b) |$
$\Rightarrow ∣ ∣ ∣ | \to c | | \to a \times \to b | cos 0^{0} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ | \to c | | \to a | | \to b | sin \frac{π}{6} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ 3 \times 4 \times 6 \times \frac{1}{2} ∣ ∣ ∣ = | 36 | = 36$

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¯ ¯ c

is perpendicular to

¯ ¯ ¯ a

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∣ ∣ ¯ ¯ ¯ a ∣ ∣ = 3, ∣ ∣ ¯ ¯ b ∣ ∣ = 4, ∣ ∣ ¯ ¯ c ∣ ∣ = 5

and the angle between

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[¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] =

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| [\to a \to b \to c] | =

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Cross Product of Two Vectors

Standard XII Mathematics

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