# What is || <-1, 9, -2 > - < 9 , -4, 1 > ||?

Mar 28, 2016

$| {V}_{r} | = \sqrt{278} \approx 16.67$

#### Explanation:

This effectively asking you to find the magnitude of the vector sum.
Solution Strategy:
1) Perform vector addition (subtraction)
2) Compute the magnitude of the new vector, ${V}_{r}$
Let $\vec{{V}_{1}} = - i + 9 j - 2 k , \mathmr{and} \vec{{V}_{2}} = 9 i - 4 j - k$
Then 1)
${V}_{r} = {V}_{1} - {V}_{2} = - i + 9 j - 2 k - \left(9 i - 4 j - k\right)$
V_r=(-1-9)I+(9-(-4)j +(-2-1)k
${V}_{r} = - 10 i + 13 j - 3 k$
and 2)
$| {V}_{r} | = \sqrt{\left(- {10}^{2} + {13}^{2} + {3}^{2}\right)} = \sqrt{278}$