To find the results of the given vector subtractions, follow these steps:
1. Calculate [tex]\(-w\)[/tex]:
Given [tex]\( w = \langle -5, 3 \rangle \)[/tex], to find [tex]\(-w\)[/tex], we multiply each component by [tex]\(-1\)[/tex]:
[tex]\[
-w = \langle -(-5), -(3) \rangle = \langle 5, -3 \rangle
\][/tex]
2. Calculate [tex]\(-w - z\)[/tex]:
Now, using [tex]\(-w = \langle 5, -3 \rangle\)[/tex] and [tex]\(z = \langle 1, 4 \rangle\)[/tex], we perform the vector subtraction:
[tex]\[
-w - z = \langle 5 - 1, -3 - 4 \rangle = \langle 4, -7 \rangle
\][/tex]
So, [tex]\(-w - z = \langle 4, -7 \rangle\)[/tex].
3. Calculate [tex]\(z - w\)[/tex]:
Given [tex]\(z = \langle 1, 4 \rangle\)[/tex] and [tex]\(w = \langle -5, 3 \rangle\)[/tex], we perform the vector subtraction:
[tex]\[
z - w = \langle 1 - (-5), 4 - 3 \rangle = \langle 1 + 5, 4 - 3 \rangle = \langle 6, 1 \rangle
\][/tex]
So, [tex]\(z - w = \langle 6, 1 \rangle\)[/tex].
4. Calculate [tex]\(w - z\)[/tex]:
Given [tex]\(w = \langle -5, 3 \rangle\)[/tex] and [tex]\(z = \langle 1, 4 \rangle\)[/tex], we perform the vector subtraction:
[tex]\[
w - z = \langle -5 - 1, 3 - 4 \rangle = \langle -6, -1 \rangle
\][/tex]
So, [tex]\(w - z = \langle -6, -1 \rangle\)[/tex].
Thus, the correct answers are:
[tex]\[
\begin{array}{l}
-w - z = \langle 4, -7 \rangle \\
z - w = \langle 6, 1 \rangle \\
w - z = \langle -6, -1 \rangle \\
\end{array}
\][/tex]
