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 C 12√(3) [a⃗b⃗c⃗] = #160;a⃗· (b⃗× #160;c⃗) = #160;a⃗· (|b⃗||c⃗| sin2π3n̂ ) = |a⃗||b⃗||c⃗| (sin2π3 ) = 2× ...

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Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

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 C $12 \sqrt{3}$
$[\to a \to b \to c] = \to a \cdot (\to b \times \to c)$
$= \to a \cdot (| \to b | | \to c | sin \frac{2 π}{3}^n)$
$= | \to a | | \to b | | \to c | (sin \frac{2 π}{3})$
$= 2 \times 3 \times 4 \times \frac{\sqrt{3}}{2} = 12 \sqrt{3}$

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Similar questions

Q. 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

\frac{2 π}{3}

, then

[\to a

\to b

\to c]

is equal to

Q. If

| \to a | = 3, ∣ ∣ \to b ∣ ∣ = 4, | \to c | = 5, \to a ⊥ (\to b + \to c), \to b ⊥ (\to c + \to a)

and

\to c ⊥ (\to a + \to b)

then

\sqrt{2} ∣ ∣ \to a + \to b + \to c ∣ ∣

is equal to

Q. Let

\to a, \to b

and

\to c

be three vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

and

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

, then

| \to a \times (\to b \times \to c) |

is equal to

Q. Let

∣ \to a ∣= 1, ∣ \to b ∣= 2

and

∣ \to c ∣= 3

and

\to a, \to b, \to c

be threee non-coplanar vectors. If

∣ \to d ∣= 4

, then

∣ \frac{[\to d \to b \to c] \to a + [\to d \to c \to a] \to b + [\to d \to a \to b] \to c}{[\to a \to b \to c]} ∣

is equal to

Q. Magnitudes of vectors

\to a, \to b, \to c

are

3, 4, 5

respectively. If

\to a

and

\to b + \to c

\to b

and

\to c + \to a

\to c

and

\to a + \to b

are mutually perpendicular, then the magnitude of

\to a + \to b + \to c

is,

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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 C 12√3[→a→b→c]=→a⋅(→b×→c)=→a⋅(|→b||→c|sin2π3^n)=|→a||→b||→c|(sin2π3)=2×3×4×√32=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

The correct option is C $12 \sqrt{3}$
$[\to a \to b \to c] = \to a \cdot (\to b \times \to c)$
$= \to a \cdot (| \to b | | \to c | sin \frac{2 π}{3}^n)$
$= | \to a | | \to b | | \to c | (sin \frac{2 π}{3})$
$= 2 \times 3 \times 4 \times \frac{\sqrt{3}}{2} = 12 \sqrt{3}$