Lesson 12 The Arithmetic of Vectors Solidify Understanding

Ready

1.

Given Point $A (3, 4)$ . Plot the points described on the coordinate grid.

Point $B$ is the image of point $A$ after a $90 °$ rotation counterclockwise about the origin.
Point $C$ is the image of point $A$ after a $180 °$ rotation counterclockwise about the origin.
Write the equation of the circle that contains points $A$ , $B$ , and $C$ .

Set

Two vectors are described in component form in the following way:

$\vec{v} : ⟨ - 2, 3 ⟩$ and $\vec{w} : ⟨ 3, 4 ⟩$ .

On the grids, create vector diagrams to show the result of the vector arithmetic, and provide the components of the resulting vector.

2.

$\vec{v} + \vec{w} = \underset{―}{}$

3.

$\vec{v} - \vec{w} = \underset{―}{}$

4.

$3 \vec{v} = \underset{―}{}$

5.

$- 2 \vec{w} = \underset{―}{}$

6.

$3 \vec{v} - 2 \vec{w} = \underset{―}{}$

7.

Show how to find $\vec{v} + \vec{w}$ using the parallelogram rule.

$\vec{v} + \vec{w} = \underset{―}{}$

Go

$A = [\begin{array}{rr} 2 & - 3 \\ - 1 & 5 \end{array}]$ , $B = [\begin{array}{rr} 2 & 5 \\ - 3 & 2 \end{array}]$ , and $C = [\begin{array}{rrr} 4 & 2 & - 1 \\ 5 & 2 & 3 \end{array}]$

Find the following sums, differences, or products, as indicated. If the sum, difference, or product is undefined, explain why.

8.

$A + B$

9.

$A + C$

10.

$2 A - B$

11.

$A \cdot B$

12.

$B \cdot A$

13.

$A \cdot C$

14.

$C \cdot A$