# Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate B-C?

Mar 20, 2018

The resultant vector is $< - 5 , 4 , 0 >$.

#### Explanation:

To subtract two vectors, it is sometimes easier to add the opposite vector. What I mean by that is:

$\vec{a} - \vec{b} q \quad q \quad \implies q \quad q \quad \vec{a} + \left(- \vec{b}\right)$

So in this case:

$\textcolor{w h i t e}{=} \vec{B} - \vec{C}$

$= < - 2 , 5 , 1 > - < 3 , 1 , 1 >$

$= < - 2 , 5 , 1 > + \left(- 1 < 3 , 1 , 1 >\right)$

$= < - 2 , 5 , 1 > + < - 3 , - 1 , - 1 >$

$= < \left(- 2 - 3\right) , \quad \left(5 - 1\right) , \quad \left(1 - 1\right) >$

$= < - 5 , 4 , 0 >$

That's the resultant vector. Hope this helped!