Question

both u - v and u + (-1v) produce the same resultant vector, which is <5, -8>. based on this compari and v, the resultant vector for u - v is the same as the resultant vector for u + (-v). part e add vector v to its negative counterpart (-1v) and write the resulting vector.

Explanation:

Step1: Recall Vector Addition

For any vector \(\mathbf{v}=\langle v_1, v_2
angle\), its negative counterpart \(-1\mathbf{v}=\langle -v_1, -v_2
angle\). When adding \(\mathbf{v}\) and \(-1\mathbf{v}\), we use the rule for vector addition: \(\mathbf{v}+(-1\mathbf{v})=\langle v_1+(-v_1), v_2+(-v_2)
angle\).

Step2: Simplify the Components

Simplify each component: \(v_1 + (-v_1)=0\) and \(v_2+(-v_2) = 0\). So the resultant vector is \(\langle0, 0
angle\), which is the zero vector.

Answer:

\(\langle 0, 0
angle\) (or the zero vector)