Question

select the correct answer from each drop - down menu.
find the results of the given vector subtractions for \\( \mathbf{u} = \langle - 8, 4 \
angle \\) and \\( \mathbf{v} = \langle 2, 7 \
angle \\).
\\( -\mathbf{u} - \mathbf{v} = \\)
\\( \mathbf{u} - \mathbf{v} = \\)
\\( \mathbf{v} - \mathbf{u} = \\)

Explanation:

Step1: Recall vector subtraction rule

For vectors \(\mathbf{u}=\langle u_1, u_2
angle\) and \(\mathbf{v}=\langle v_1, v_2
angle\), \(\mathbf{u}-\mathbf{v}=\langle u_1 - v_1, u_2 - v_2
angle\), and \(-\mathbf{u}=\langle -u_1, -u_2
angle\).

Step2: Calculate \(-\mathbf{u}-\mathbf{v}\)

Given \(\mathbf{u}=\langle - 8,4
angle\), so \(-\mathbf{u}=\langle8,-4
angle\). \(\mathbf{v}=\langle2,7
angle\). Then \(-\mathbf{u}-\mathbf{v}=\langle8 - 2,-4 - 7
angle=\langle6,-11
angle\).

Step3: Calculate \(\mathbf{u}-\mathbf{v}\)

Using the rule, \(\mathbf{u}-\mathbf{v}=\langle-8 - 2,4 - 7
angle=\langle-10,-3
angle\).

Step4: Calculate \(\mathbf{v}-\mathbf{u}\)

\(\mathbf{v}-\mathbf{u}=\langle2-(-8),7 - 4
angle=\langle10,3
angle\).

Answer:

For \(-\mathbf{u}-\mathbf{v}\), the result is \(\langle6,-11
angle\); for \(\mathbf{u}-\mathbf{v}\), the result is \(\langle-10,-3
angle\); for \(\mathbf{v}-\mathbf{u}\), the result is \(\langle10,3
angle\).