CameraIcon

SearchIcon

MyQuestionIcon

1

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

Bisector of Angle between Two Vectors

Unit vector ...

Question

Unit vector $\to r$ which satisfies $\to r \times \to b = \to r \times \to c$ where $\to b = ˆ i + 2 ˆ j + ˆ k$ & $\to c = 3 ˆ i + 2 ˆ k$ , is

A

\pm (\frac{2 ˆ i - 2 ˆ j + ˆ k}{3})

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

B

\pm (\frac{2 ˆ i + 2 ˆ j + ˆ k}{3})

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

C

\pm (\frac{ˆ i + ˆ j + ˆ k}{\sqrt{3}})

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

D

\pm ˆ i

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

Open in App

Solution

The correct option is B $\pm (\frac{2 ˆ i - 2 ˆ j + ˆ k}{3})$
Given $\to b = ˆ i + 2 ˆ j + ˆ k$ & $\to c = 3 ˆ i + 2 ˆ k$
$\to r \times \to b = \to r \times \to c$
$(\to r \times \to b) - (\to r \times \to c) = \to 0$
$\Rightarrow \to r \times (\to b - \to c) = \to 0$
$\Rightarrow \to r = λ (\to b - \to c) = λ (- 2 ˆ i + 2 ˆ j - ˆ k)$
$\Rightarrow ˆ r = \pm (\frac{2 ˆ i - 2 ˆ j + ˆ k}{3})$

Suggest Corrections

thumbs-up

0

Similar questions

\to r \times \to b = \to c \times \to b & \to r, \to a = 0

\to a = 2 \land i + 3 \land j - \land k, \to b = 3 \land i - \land j - k, \to c = \land i + \land j + \land k

\to r

\to a = ˆ i + ˆ j

\to b = 2 ˆ i - ˆ k

\to r

satisfying the equations

\to r \times \to a = \to b \times \to a

\to r \times \to b = \to a \times \to b

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

\to c = λ ˆ i + ˆ j + 2 ˆ k

are coplanar, then find the value of

(λ - 4)

\to a = ˆ i, \to b = - \frac{1}{2} ˆ i + \frac{\sqrt{3}}{2} ˆ j

ˆ c = - \frac{1}{2} ˆ i - \frac{\sqrt{3}}{2} ˆ j

are three coplanar unit vectors such that

\to a + \to b + \to c = 0

. If three other vectors

\to p, \to q

\to r

are parallel to

\to a, \to b

\to c

, respectively, and have integral but different magnitudes, then among the following options,

| \to p + \to q + \to r |

can take a value equal to

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Application of Vectors - Lines

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Bisector of Angle between Two Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon