Question

drag the tiles to the boxes to form correct pairs.
let (mathbf{u} = langle -5, 2
angle), (mathbf{v} = langle -1, -3
angle), and (mathbf{w} = langle 3, -4
angle). find the resultant of each statement.
tiles
(langle -22, 20
angle) (langle 2, -3
angle) (langle -12, 3
angle)
pairs
(-2mathbf{u} + mathbf{v}) (longleftrightarrow) (langle 9, -7
angle)
(3mathbf{v} - 3mathbf{w}) (longleftrightarrow) blank
(mathbf{u} - mathbf{v} + 2mathbf{w}) (longleftrightarrow) blank
(2mathbf{u} - 4mathbf{w}) (longleftrightarrow) blank

Explanation:

Step1: Calculate \(3\mathbf{v} - 3\mathbf{w}\)

Given \(\mathbf{v}=\langle - 1,-3
angle\) and \(\mathbf{w}=\langle3,-4
angle\). First, find \(3\mathbf{v}\) and \(3\mathbf{w}\):
\(3\mathbf{v}=3\langle - 1,-3
angle=\langle3\times(-1),3\times(-3)
angle=\langle - 3,-9
angle\)
\(3\mathbf{w}=3\langle3,-4
angle=\langle3\times3,3\times(-4)
angle=\langle9,-12
angle\)
Then \(3\mathbf{v}-3\mathbf{w}=\langle - 3 - 9,-9-(-12)
angle=\langle - 12,3
angle\)

Step2: Calculate \(\mathbf{u}-\mathbf{v}+2\mathbf{w}\)

Given \(\mathbf{u}=\langle - 5,2
angle\), \(\mathbf{v}=\langle - 1,-3
angle\), \(\mathbf{w}=\langle3,-4
angle\).
First, find \(-\mathbf{v}=\langle1,3
angle\) and \(2\mathbf{w}=\langle6,-8
angle\)
Then \(\mathbf{u}-\mathbf{v}+2\mathbf{w}=\langle - 5,2
angle+\langle1,3
angle+\langle6,-8
angle=\langle - 5 + 1+6,2 + 3-8
angle=\langle2,-3
angle\)

Step3: Calculate \(2\mathbf{u}-4\mathbf{w}\)

Given \(\mathbf{u}=\langle - 5,2
angle\), \(\mathbf{w}=\langle3,-4
angle\)
\(2\mathbf{u}=2\langle - 5,2
angle=\langle - 10,4
angle\)
\(4\mathbf{w}=4\langle3,-4
angle=\langle12,-16
angle\)
\(2\mathbf{u}-4\mathbf{w}=\langle - 10-12,4-(-16)
angle=\langle - 22,20
angle\)

Answer:

• \(3\mathbf{v}-3\mathbf{w}\) pairs with \(\langle - 12,3

angle\)

• \(\mathbf{u}-\mathbf{v}+2\mathbf{w}\) pairs with \(\langle2,-3

angle\)

• \(2\mathbf{u}-4\mathbf{w}\) pairs with \(\langle - 22,20

angle\)