Question

A unit vector in the direction of resultant vector of is

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

Here, $\overrightarrow { \mathrm { A } } = - 2 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } + \hat { \mathrm { k } }$

The resultant vector of and $\vec { B }$ is

= $( - 2 \hat { i } + 3 \hat { j } + \hat { k } ) + ( \hat { i } + 2 \hat { j } - 4 \hat { k } ) = - \hat { i } + 5 \hat { j } - 3 \hat { k }$ $| \overrightarrow { \mathrm { R } } | = \sqrt { ( - 1 ) ^ { 2 } + ( 5 ) ^ { 2 } + ( - 3 ) ^ { 2 } } = \sqrt { 1 + 25 + 9 } = \sqrt { 35 }$

Units vector in the directions of resultant vector or $\vec { A }$ and is

$\hat { R } = \frac { \vec { R } } { | \vec { R } | } = \frac { - \hat { i } + 5 \hat { j } - 3 \hat { k } } { \sqrt { 35 } }$