MyQuestionIcon

1

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

Collinear Vectors

If a, b and c...

Question

If $\to a, \to b$ and $\to c$ are any three non-zero vectors in space, then the value of $(\to c + \to b) \times (\to c + \to a) \cdot (\to c + \to b + \to a)$ is :

A

[\to a \to b \to c]

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

B

2 [\to a \to b \to c]

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

C

0

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

D

3 [\to a \to b \to c]

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

Open in App

Solution

The correct option is A $[\to a \to b \to c]$
Let $E = (\to c + \to b) \times (\to c + \to a) \cdot (\to c + \to b + \to a)$
$\Rightarrow E = (\to c \times \to c + \to c \times \to a + \to b \times \to c + \to b \times \to a) \cdot (\to c + \to b + \to a)$
Since $\to c \times \to c = \to 0$ ,
$\Rightarrow E = (\to c \times \to a + \to b \times \to c + \to b \times \to a) \cdot (\to c + \to b + \to a)$
On multiplying (taking dot product) term by term, we have
$\Rightarrow E = \to b \times \to a \cdot \to c + \to c \times \to a \cdot \to b + \to b \times \to c \cdot \to a$
$\Rightarrow E = - [\to a \to b \to c] + [\to a \to b \to c] + [\to a \to b \to c]$
$\Rightarrow E = [\to a \to b \to c]$

Suggest Corrections

thumbs-up

1

Similar questions

\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

are three non zero vectors such that any two of them are non-collinear. If

\to a + \to b

is collinear with

\to c

\to b + \to c

is collinear with

\to a

, then the value of

\to a + \to b + \to c

\to a, \to b, \to c

be any three non - coplanar vectors, then calculate the value of

[\to a + \to b \to b + \to c \to c + \to a]

\to a, \to b, \to c

are any three vectors in space then

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

\to a, \to b

\to c

are three non-zero vectors such that

\to a . \to b = \to a . \to c,

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Collinear Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon