q = $\left(\begin{array}{c}-2\\ 3\end{array}\right)$

r = $\left(\begin{array}{c}3\\ -2\end{array}\right)$

q - r = $\left(\begin{array}{c}-2\\ 3\end{array}\right)$ - $\left(\begin{array}{c}3\\ -2\end{array}\right)$

q - r = $\left(\begin{array}{c}\mathrm{-2\; -\; 3}\\ \mathrm{3-(-2)}\end{array}\right)$

q - r = $\left(\begin{array}{c}-5\\ \mathrm{3+2}\end{array}\right)$

q - r = $\left(\begin{array}{c}-5\\ 5\end{array}\right)$

If AB is a vector from A to B, then its negative vector is BA and it is from B to A. i.e., just multiplying by a negative sign changes the direction of the vector. In this case, we can say AB = - BA and BA = - AB. Also, |AB| = |BA|. Hence, AB and BA are the negatives of each other.

Negating A Vector

NOTE: - x - = +

Applying the addition rule

Now add a and b

a = $\left(\begin{array}{c}3\\ 1\end{array}\right)$ and b = $\left(\begin{array}{c}-2\\ 1\end{array}\right)$

6b + 2a = 6$\left(\begin{array}{c}-2\\ 1\end{array}\right)$ + 2$\left(\begin{array}{c}3\\ 1\end{array}\right)$

The number outside multiplies each element inside.

6b + 2a = $\left(\begin{array}{c}\mathrm{-2\; x\; 6}\\ \mathrm{1\; x\; 6}\end{array}\right)$ + $\left(\begin{array}{c}\mathrm{3\; x\; 2}\\ \mathrm{1\; x\; 2}\end{array}\right)$

6b + 2a = $\left(\begin{array}{c}-12\\ 6\end{array}\right)$ + $\left(\begin{array}{c}6\\ 2\end{array}\right)$

Add the corresponding elements. Top row to top row, bottom row to bottom row.

6b + 2a = $\left(\begin{array}{c}\mathrm{-12\; +\; 6}\\ \mathrm{6\; +\; 2}\end{array}\right)$

6b + 2a = $\left(\begin{array}{c}-6\\ 8\end{array}\right)$