Question

if ( mathbf{c}=langle-4,7
angle ) and ( mathbf{d}=langle 8,-6
angle ), find the sum ( mathbf{c}+mathbf{d} ).
( mathbf{c}+mathbf{d}=langlesquare,square
angle )

Explanation:

Step1: Add the x - components

For vectors \(\mathbf{c}=\langle - 4,7
angle\) and \(\mathbf{d}=\langle8,-6
angle\), the x - component of \(\mathbf{c}+\mathbf{d}\) is obtained by adding the x - components of \(\mathbf{c}\) and \(\mathbf{d}\).
The x - component of \(\mathbf{c}\) is \(-4\) and the x - component of \(\mathbf{d}\) is \(8\). So, \(-4 + 8\).

$$ -4+8=4 $$

Step2: Add the y - components

The y - component of \(\mathbf{c}\) is \(7\) and the y - component of \(\mathbf{d}\) is \(-6\). So, \(7+( - 6)\).

$$ 7+( - 6)=7 - 6=1 $$

Answer:

\(\langle4,1
angle\)