If a = 2i+j+k and b = i+2j+3k, then the magnitude of the vec... | Mathematics - Vectors and their Properties | SolveeIt | Solveeit

Today, August 19

Question

If a = 2i+j+k and b = i+2j+3k, then the magnitude of the vector $(\overline{a+b})$ is

Visual representation for Mathematics

A

$\sqrt{6}$

B

$\sqrt{34}$

C

$\sqrt{14}$

D

$\sqrt{26}$

Answer

$\sqrt{34}$

Explanation

Solution

Given:

\vec{a} = 2\hat{i}+\hat{j}+\hat{k},\quad \vec{b} = \hat{i}+2\hat{j}+3\hat{k}

Then,

\vec{a}+\vec{b} = (2+1)\hat{i}+(1+2)\hat{j}+(1+3)\hat{k} = 3\hat{i}+3\hat{j}+4\hat{k}

Magnitude:

|\vec{a}+\vec{b}| = \sqrt{3^2+3^2+4^2} = \sqrt{9+9+16} = \sqrt{34}