CameraIcon

SearchIcon

MyQuestionIcon

1

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

Vector Triple Product

If a, b, c ar...

Question

If $\to a, \to b, \to c$ are three non coplanar vectors and a vector $\to r$ satisfying the vector equation $\to r . \to a = \to r . \to b = \to r . \to c = 1$ is:

A

\frac{1}{[\to a \to b \to c]} ((\to a \cdot \to b) + (\to b \cdot \to c) + (\to c \cdot \to a))

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

B

\frac{1}{[\to a \to b \to c]} ((\to a \times \to b) + (\to b \times \to c) + (\to a \times \to c))

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

C

\frac{(\to a \times \to b)}{[\to a \to b \to c]} + \frac{(\to c \times \to b)}{[\to a \to b \to c]} + \frac{(\to c \times \to a)}{[\to a \to b \to c]}

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

D

\frac{(\to a \times \to b) + (\to b \times \to c) + (\to c \times \to a)}{[\to a \to b \to c]}

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

Open in App

Solution

The correct option is D $\frac{(\to a \times \to b) + (\to b \times \to c) + (\to c \times \to a)}{[\to a \to b \to c]}$
Since $\to a, \to b, \to c$ are three non coplanar vectors, therefore $(\to a \times \to b), (\to b \times \to c), (\to c \times \to a)$ are also non coplanar vectors.
Let $\to r = x (\to a \times \to b) + y (\to b \times \to c) + z (\to c \times \to a)$
Then $\to r . \to a = 1 \Rightarrow 1 = y [\to a \to b \to c]$
$\Rightarrow y = \frac{1}{[\to a \to b \to c]}$
Similarly, $\to r . \to b = 1 \Rightarrow 1 = z [\to a \to b \to c]$
$\Rightarrow z = \frac{1}{[\to a \to b \to c]}$
and $\to r . \to c = 1 \Rightarrow 1 = x [\to a \to b \to c]$
$\Rightarrow x = \frac{1}{[\to a \to b \to c]}$

Suggest Corrections

thumbs-up

1

Similar questions

\to a, \to b, \to c

are non-coplanar vectors

\to r . \to a = \to r . \to b = \to r . \to c = 0

\to r

is a zero vector.

\to a, \to b, \to c

are three non coplanar vectors and a vector

\to r = \frac{(\to r . \to a) (\to b \times \to c) + (\to r . \to b) (\to c \times \to a) + (\to r . \to c) (\to a \times \to b)}{λ},

then the value of

λ

\to a, \to b, \to c

are three non coplanar, non zero vectors and

\to r

is any vector in space, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

λ [\to a \to b \to c]

. Then the value of

λ

\to a, \to b, \to c

be three non-coplanar vectors and

\to r

be any vector in space such that

\to r . \to a = 1, \to r . \to b = 2

\to r . \to c = 3.

[\to a, \to b, \to c] = 1

\to r

\to a, \to b, \to c

\to p, \to q, \to r

are sets of three non-coplanar unit vectors such that

\to a \cdot \to p + \to b \cdot \to q + \to c \cdot \to r = 3,

\to p, \to q

\to r

respectively are given by the vectors

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Vector Triple Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon