CameraIcon

CameraIcon

SearchIcon

MyQuestionIcon

MyQuestionIcon

Multiplication with Vectors

If a, b, c be...

Question

If $\to a, \to b, \to c$ be any three non - coplanar vectors, then calculate the value of $[\to a + \to b \to b + \to c \to c + \to a]$ is

A

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

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

B

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

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

C

2 \sqrt{[\to a + \to b + \to c]}

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

D

[\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 B $2 [\to a \to b \to c]$
$[\to a + \to b \to b + \to c \to c + \to a] = (\to a + \to b) . {(\to b + \to c) \times (\to c + \to a)}$
$= (\to a + \to b) . (\to b \times \to c + \to b \times \to a + \to c \times \to c + \to c \times \to a)$
$= (\to a + \to b) . (\to b \times \to c + \to b \times \to a + \to c \times \to a)$
$= \to a (\to b \times \to c) + \to a (\to b \times \to a) + \to a . (\to c \times \to a) + \to b . (\to b \times \to c) + \to b (\to b \times \to a) + \to b . (\to c \times \to a)$
$= [\to a \to b \to c] + [\to b \to c \to a]$
$= 2 [\to a \to b \to c]$

Suggest Corrections

thumbs-up

0

mid-banner-image

mid-banner-image

Similar questions

\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

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

be three non-coplanar vectors and

\to r

be any arbitrary vector, 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)

Q. Assertion :If

a, b, c

are three non-coplanar, non-zero vectors, then

(a . a) b \times c + (a . b) c \times a + (a . c) a \times b = [b c a] a

Reason: If the vectors

a, b, c

are non-coplanar, then so are

b \times c, c \times a, a \times b

A, B, C

are three non-coplanar vectors, then find the value of

\frac{A \cdot (B \times C)}{(C \times A) \cdot B} + \frac{B \cdot (A \times C)}{C \cdot (A \times B)}

View More

similar_icon

Related Videos

lock

PHYSICS

Watch in App

Explore more

Multiplication with Vectors

Standard XI Physics