MyQuestionIcon

1

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

Cross Product of Two Vectors

Let a⃗, b⃗ ...

Question

Let $\to a, \to b$ and $\to c$ be non-zero vectors such that $(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a$ . If $θ$ is the acute angle between the vectors $\to b$ and $\to c$ , then $sin θ$ equals?

A

\frac{1}{3}

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

B

\frac{\sqrt{2}}{3}

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

C

\frac{2}{3}

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

D

\frac{2 \sqrt{2}}{3}

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

Open in App

Solution

The correct option is D $\frac{2 \sqrt{2}}{3}$
$\begin{matrix} (\to a \times \to b) \times \to c = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a - \to c (\to a \times \to b) = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a - [(\to c \times \to b) \to a - (\to c \times \to a) \to b] = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a (\to c \times \to a) \to b - (\to c \times \to b) \to a = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a - (\to c \times \to b) \to a = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a - ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a cos θ = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a cos θ = - \frac{1}{3} sin θ = \frac{2 \sqrt{2}}{3} \end{matrix}$
Option $D$ is correct.

Suggest Corrections

thumbs-up

0

Similar questions

\to a, \to b

\to c

be non-zero vectors such that

(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a

θ

is the acute angle between the vectors

¯ ¯ ¯ b

¯ ¯ ¯ c

sin θ

\to a, \to b

\to c

be non-zero vectors such that

\to a

\to b

are non-collinear & satisfies

(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a

θ

is the angle between the vectors

\to b

\to c

sin θ

\to a, \to b

\to c

be three non-zero vectors such that no two of them are collinear and

(\to a \times \to b) \times \to c = \frac{1}{3} ∣ ∣ \to b ∣ ∣ | \to c | \to a

θ

is the angle between vectors

\to b

\to c

, then a value of

sin θ

\to a, \to b

\to c

be three non-zero vectors such that no two of them are collinear and

(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a

θ

is the angle between vectors

\to b

\to c

, then a value of

sin θ

\to a

\to b

\to c

be non-zero vectots such that (

\to a

\to b

\to c

\frac{1}{3}

∣ ∣ \to b ∣ ∣ | \to c | \to a

θ

is the acute angle between the

\to b

\to c

θ

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Vector Product

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Cross Product of Two Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon