Question

if ( mathbf{a}=(8,-1) ) and ( mathbf{b}=(-6,3) ), find the sum ( mathbf{a}+mathbf{b} ). ( mathbf{a}+mathbf{b}=langlequad,quad
angle )

Explanation:

Step1: Add the x - components

For vectors \(\mathbf{a}=\langle x_1,y_1
angle\) and \(\mathbf{b}=\langle x_2,y_2
angle\), the sum \(\mathbf{a}+\mathbf{b}=\langle x_1 + x_2,y_1 + y_2
angle\).
Here \(x_1 = 8\) (from \(\mathbf{a}=\langle8,-1
angle\)) and \(x_2=-6\) (from \(\mathbf{b}=\langle - 6,3
angle\)).
\(x_1+x_2=8+( - 6)=2\)

Step2: Add the y - components

\(y_1=-1\) (from \(\mathbf{a}=\langle8,-1
angle\)) and \(y_2 = 3\) (from \(\mathbf{b}=\langle - 6,3
angle\)).
\(y_1 + y_2=-1 + 3=2\)

Answer:

\(\langle2,2
angle\)