MyQuestionIcon

4

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Vector Triple Product

If x×y=a, y×z...

Question

If $\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1$ and $\to y \cdot \to z = 1$ . Vector $\to x$ is

A

\frac{1}{| \to a \times \to b |^{2}} [\to a \times (\to a \times \to b)]

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

B

\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b - \to a \times (\to a \times \to b)]

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

C

\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b + \to b \times (\to a \times \to b)]

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

D

None of these

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

Open in App

Solution

The correct option is B $\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b - \to a \times (\to a \times \to b)]$
$\to x \times \to y = \to a (i)$
$\to y \times \to z = \to b (i i)$
$\to x \cdot \to b = γ (i i i)$
$\to x \cdot \to y = 1 (i v)$
$\to y \cdot \to z = 1 (v)$

From $(i i)$ , $\to x \cdot (\to y \times \to z) = \to x \cdot \to b = γ$
$\Rightarrow [\to x \to y \to z] = γ$

From $(i)$ and $(i i)$ ,
$(\to x \times \to y) \times (\to y \times \to z) = \to a \times \to b$
$∴ [\to x \to y \to z] \to y - [\to y \to y \to z] \to x = \to a \times \to b$
or $\to y = \frac{\to a \times \to b}{γ} (v i)$

Also from $(i)$ , we get $(\to x \times \to y) \times \to y = \to a \times \to y$
$(\to x \cdot \to y) \to y - (\to y \cdot \to y) \to x = \to a \times \to y$

$\to x = \frac{1}{| \to y |^{2}} (\to y - \to a \times \to y)$

$= \frac{γ}{| \to a \times \to b |^{2}} ⎡ ⎢ ⎣ \frac{\to a \times \to b}{γ} - \frac{\to a \times (\to a \times \to b)}{γ} ⎤ ⎥ ⎦$

$= \frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b - \to a \times (\to a \times \to b)]$

Suggest Corrections

thumbs-up

0

Similar questions

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

\to y \cdot \to z = 1

\to y

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

\to y \cdot \to z = 1

\to z

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

\to y \cdot \to z = 1

\to x

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

\to y \cdot \to z = 1

\to y

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

\to y \cdot \to z = 1

\to z

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Vector Triple Product

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Vector Triple Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon