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

Unit Vectors

If A -4,0,3...

Question

If $A (- 4, 0, 3); B (14, 2, - 5)$ then which one of the following points lie on the bisector of the angle between $\to O A$ and $\to O B$ (' $O$ ' is the origin of reference)

(2, 1, - 1)

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

(2, 11, 5)

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

(10, 2, - 2)

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

(1, 1, 2)

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

Open in App

Solution

The correct option is D $(1, 1, 2)$
$O$ is the origin.
So the internal angle bisector of $∠ A O B$ will be given by the sum of unit vectors along the $O A$ and $O B$ directions.
Thus, $\frac{- 4^i + 3^k}{5} + \frac{14^i + 2^j - 5^k}{15} = \frac{2^i + 2^j + 4^k}{15}$

Thus, any point in the multiple of $(2, 2, 4)$ will lie on the angle bisector.

Suggest Corrections

Similar questions

\to O A = \to a

\to O B = \to b

∠ A O B

Δ O A B

\to O A = \to a, \to O B = \to b . L

\to O A

M

\to O B

\to O M : \to M B = 2 : 1

P

L M

\to A P =

A B C D

O

\to O A + \to O B + \to O C + \to O D

A, B, C

^i +^j,^i -^j

l^i + m^j + n^k

O

\to O A, \to O B, \to O C

A C

O

B

1 : 2

\to O A = \to a & \to O B = \to b,

\to O C

\to a & \to b,

Join BYJU'S Learning Program