If a- is perpendicular to b- and c- -a-2- -b-3- -c-4 and the angle between b- and c- is 2-3- then -a- b- c- is equal to

The correct option is B 12√(3) Since a⃗ is pependicular to b⃗ and c⃗ ∴ a⃗=k(b⃗×c⃗) | a |=k | b⃗ | | c⃗ |sin2π3 2=k× ...

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Byju's Answer

Standard XII

Mathematics

Monotonically Increasing Functions

If a⃗ is pe...

Question

If $\to a$ is perpendicular to $\to b$ and $\to c, | \to a | = 2, | \to b | = 3, | \to c | = 4$ and the angle between $\to b$ and $\to c$ is $\frac{2 π}{3}$ , then $[\to a$ $\to b$ $\to c]$ is equal to

4 \sqrt{3}

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6 \sqrt{3}

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12 \sqrt{3}

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18 \sqrt{3}

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Solution

The correct option is B $12 \sqrt{3}$
Since $\to a$ is pependicular to $\to b$ and $\to c$
$∴$ $\to a = k (\to b \times \to c)$

$| a | = k ∣ ∣ \to b ∣ ∣ | \to c | sin \frac{2 π}{3}$
$2 = k \times 3 \times 4 \times \frac{\sqrt{3}}{2}$
$k = \frac{1}{3 \sqrt{3}}$

$[¯ a ¯ b ¯ c] = k (\to b \times \to c)^{2}$
= $\frac{1}{3 \sqrt{3}} \times 9 \times 16 \times \frac{3}{4}$
= $12 \sqrt{3}$

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Similar questions

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If →a is perpendicular to →b and →c, |→a|=2, |→b|=3, |→c|=4 and the angle between →b and →c is 2π3, then [→a →b →c] is equal to

The correct option is B 12√3Since →a is pependicular to →b and →c∴ →a=k(→b×→c)|a|=k∣∣→b∣∣|→c|sin2π32=k×3×4×√32k=13√3[¯a¯b¯c]=k(→b×→c)2=13√3×9×16×34=12√3

If $\to a$ is perpendicular to $\to b$ and $\to c, | \to a | = 2, | \to b | = 3, | \to c | = 4$ and the angle between $\to b$ and $\to c$ is $\frac{2 π}{3}$ , then $[\to a$ $\to b$ $\to c]$ is equal to