Question

directions
read the instructions for this self - checked activity. type in your response to each question, and check your answers. at the end brief evaluation of your work.

activity
in this activity, you will explore using negative vectors to subtract vectors.

part a
consider two vectors, \\(\mathbf{u} = \langle 2, - 3\
angle\\) and \\(\mathbf{v} = \langle - 3, 5\
angle\\). subtract vector \\(\mathbf{v}\\) from vector \\(\mathbf{u}\\), and write the result in component form.

Explanation:

Step1: Recall vector subtraction rule

To subtract vector \(\mathbf{v}\) from vector \(\mathbf{u}\), we use the rule \(\mathbf{u}-\mathbf{v}=\mathbf{u}+(-\mathbf{v})\). For a vector \(\mathbf{v}=\langle v_1, v_2
angle\), \(-\mathbf{v}=\langle -v_1, -v_2
angle\).
Given \(\mathbf{u}=\langle 2, - 3
angle\) and \(\mathbf{v}=\langle - 3,5
angle\), first find \(-\mathbf{v}\): \(-\mathbf{v}=\langle -(-3), - 5
angle=\langle 3, - 5
angle\).

Step2: Add \(\mathbf{u}\) and \(-\mathbf{v}\)

Now, add \(\mathbf{u}\) and \(-\mathbf{v}\) component - wise. The formula for adding two vectors \(\mathbf{a}=\langle a_1,a_2
angle\) and \(\mathbf{b}=\langle b_1,b_2
angle\) is \(\mathbf{a}+\mathbf{b}=\langle a_1 + b_1,a_2 + b_2
angle\).
So, \(\mathbf{u}+(-\mathbf{v})=\langle 2+3,-3+(-5)
angle=\langle 5,-8
angle\).

Answer:

\(\langle 5, - 8
angle\)