CameraIcon

SearchIcon

MyQuestionIcon

83

You visited us 83 times! Enjoying our articles? Unlock Full Access!

Work Done as Dot Product

Let a⃗=-î-k...

Question

Let $\to a = -^i -^k, \to b = -^i +^j$ and $\to c =^i + 2^j + 3^k$ be three given vectors. If $\to r$ is a vector such that $\to r \times \to b = \to c \times \to b$ and $\to r \cdot \to a = 0$ , then the value of $\to r \cdot \to b$ is?

A

8

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

B

9

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

C

6

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 $9$
Given $\to a = -^i -^k, \to b = -^i +^j, \to c =^i + 2^j + 3^k$
$\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$
Cross product with $\to a$ on both sides.
$\Rightarrow (\to r \times \to b) \times \to a = (\to c \times \to b) \to a$
$\Rightarrow (\to r . \to a) \to b - (\to b . \to a) \to r = (\to c . \to a) \to b - (\to b . \to a) \to c$
$\to a . \to b = (- 1) (- 1) + (1) (0) + (- 1) (0) = 1$
$\to b . \to C = (- 1) (1) + (1) (2) + (0) (3) = 1$
$\to c . \to a = (- 1) (1) + (0) (2) + (- 1) (3) = - 4$
$\Rightarrow - \to r = - 4 \to b - \to c$
$\Rightarrow \to r = 4 \to b + \to c$
$= - 4^i + 4^j +^i + 2^j + 3^k$
$= - 3^i + 6^i + 3^k$
$∴ \to r . \to b (- 3^i + 6^j + 3^k) . (-^i +^j)$
$= 3 + 6$
$= 9$

Suggest Corrections

thumbs-up

0

Similar questions

\to a = -^i -^k, \to b = -^i +^j

\to c =^i + 2^j + 3^k

be three given vectors. lf

\to r

is a vector such that

\to r \times \to b = \to c \times \to b

\to r . \to a = 0

, then the value of

\to r . \to b

\to a =^i - 2^j +^k

\to b =^i -^j +^k

be two vectors. If

\to c

is a vector such that

\to b \times \to c = \to b \times \to a

\to c \cdot \to a = 0

\to c \cdot \to b

\to a = 2^i +^k, \to b =^i +^j +^k

\to c = 4^i - 3^j + 7^k

be three vectors. The vector which satisfies

\to r \times \to b = \to c \times \to b

\to r . \to a = 0

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

\to a =^i +^j -^k, \to b = -^i + 2^j + 2^k

\to c = -^i + 2^j -^k

, find a unit vectors normal to the vectors

\to a + \to b

\to b + \to c

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

The Work Done as a Dot-Product

PHYSICS

Watch in App

explore_more_icon

Explore more

Work Done as Dot Product

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon