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× ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12 \sqrt{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

18 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

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

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

Suggest Corrections

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 ∣ ∣ = \sqrt{2}

| \to c | = \sqrt{3}

, and

\to a ⊥ (\to b + \to c)

\to b ⊥ (\to c + \to a)

and

\to c ⊥ (\to a + \to b)

, then

∣ ∣ \to a + \to b + \to c ∣ ∣

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,

Join BYJU'S Learning Program

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