Question

find each quantity if $v=3i-5j$and $w=-2i+3j$

$\left|\left|v+w\right|\right|$

Short answer

The value of $\left|\left|v+w\right|\right|$when $v=3i-5j$ and $w=-2i+3j$ is $\sqrt{5}$

Step-by-step solution

Step 1. Given data 

$v=3i-5j$and $w=-2i+3j$

Step 2. Find the exact valueSubstitute the values of v and w in the equation v+w

$v+w=3i-5j-2i+3j$

$v+w=i-2j$

Step 3. Find the magnitude 

$\left|\left|v+w\right|\right|=\sqrt{1^2+2^2}$

$\left|\left|v+w\right|\right|=\sqrt{1+4}$

$\left|\left|v+w\right|\right|=\sqrt{5}$