Answer:
B. The operation [tex]\bf{u}-\bf{v}[/tex] is the correct answer.
Step-by-step explanation:
Given:
[tex]{\bf u} = {<2, -5>}\\{\bf v} = <3, -2>\\{\bf w} = <5, -3>[/tex]
From the graph, we know that the vector is [tex]\langle -1,-3 \rangle[/tex].
A. The operation [tex]-\bf{v}-\bf{u}[/tex] is equal to
[tex]-\langle3,-2\rangle-\langle 2,-5\rangle\\\langle-3,2\rangle-\langle 2,-5\rangle\\\langle -3-2,2+5 \rangle\\\langle-5,7\rangle[/tex]
B. The operation [tex]\bf{u}-\bf{v}[/tex] is equal to
[tex]\langle2,-5\rangle-\langle 3,-2\rangle\\\langle 2-3,-5+2 \rangle\\\langle-1,-3\rangle[/tex]
C. The operation [tex]2\bf{w}-\bf{u}[/tex] is equal to
[tex]2\langle5,-3\rangle-\langle 2,-5\rangle\\\langle 10,-6 \rangle-\langle 2,-5 \rangle\\\langle 10-2,-6+5 \rangle\\\langle8,-1\rangle[/tex]
D. The operation [tex]-2\bf{u}[/tex] is equal to
[tex]-2\langle 2,-5\rangle\\\langle -2,10\rangle[/tex]
Therefore, the operation that gives us the vector [tex]\langle -1,-3 \rangle[/tex] is [tex]\bf{u}-\bf{v}[/tex].
