1.
- [latex]\displaystyle \|{\bf{u}}\|[/latex]
- [latex]\displaystyle 2{\bf{u}}[/latex]
- [latex]\displaystyle \|2{\bf{u}}\|[/latex]
Chapter 9: Vectors
Suggested Homework Problems
For Problems 1–4, give the coordinate form of each vector shown in the figure. Use the coordinate form to find the following.
Which of the following statements is true?
For Problems 7–10,
The displacement vector from [latex](1,-2)[/latex] to [latex](-4,6)\text{.}[/latex]
The displacement vector from [latex](-5,2)[/latex] to [latex](4,7)\text{.}[/latex]
The displacement vector from [latex](-2,9)[/latex] to [latex](-4,8)\text{.}[/latex]
The displacement vector from [latex](-6,2)[/latex] to [latex](3,0)\text{.}[/latex]
Hermione is 12 meters east and 3 meters north of Harry. Ron is 6 meters east and 9 meters north of Hermione.
Delbert and Francine are climbing a rock wall. Delbert is 8 feet to the right and 23 feet above their starting point. Francine is 2 feet to the right and 7 feet above Delbert.
For Problems 13–18, find the magnitude and direction of the vector.
[latex]{\bf{v}} = -6{\bf{i}}+6{\bf{j}}[/latex]
[latex]{\bf{p}} = -12{\bf{i}}-5{\bf{j}}[/latex]
[latex]{\bf{w}} = 7\sqrt{3}{\bf{i}}-7{\bf{j}}[/latex]
[latex]{\bf{z}} = -6\sqrt{2}{\bf{i}}+6\sqrt{6}{\bf{j}}[/latex]
[latex]{\bf{q}} = 52{\bf{i}}+96{\bf{j}}[/latex]
[latex]{\bf{s}} = 3.2{\bf{i}}-1.8{\bf{j}}[/latex]
For Problems 19–22, find the coordinate form of the vector.
[latex]\|{\bf{v}}\|=6,~\theta = -45°[/latex]
[latex]\|{\bf{v}}\|=200,~\theta = 240°[/latex]
[latex]\|{\bf{v}}\|=8.3,~\theta = 37°[/latex]
[latex]\|{\bf{v}}\|=23,~\theta = 200°[/latex]
For Problems 23–26, sketch each vector and its components. Use the coordinate form to find the resultant vector [latex]{\bf{u}}+{\bf{v}}\text{,}[/latex] and sketch it.
[latex]{\bf{u}} = -3{\bf{i}}+2{\bf{j}},~{\bf{v}} = 4{\bf{i}}-4{\bf{j}}[/latex]
[latex]{\bf{u}}= 5{\bf{i}}+{\bf{j}},~{\bf{v}} = 2{\bf{i}}-3{\bf{j}}[/latex]
[latex]{\bf{u}}= -5{\bf{i}}-2{\bf{j}},~{\bf{v}} = {\bf{i}}+6{\bf{j}}[/latex]
[latex]{\bf{u}}=8{\bf{i}}-3{\bf{j}},~{\bf{v}}= -4{\bf{i}}-2{\bf{j}}[/latex]
For Problems 27–30, find the sum [latex]{\bf{u}}+{\bf{v}}[/latex] of the given vectors.
[latex]{\bf{u}}=13{\bf{i}}-8{\bf{j}},~{\bf{v}}= -1{\bf{i}}+11{\bf{j}}[/latex]
[latex]{\bf{u}}=3.7{\bf{i}}+2.6{\bf{j}},~{\bf{v}}=-1.3{\bf{i}}-5.7{\bf{j}}[/latex]
[latex]{\bf{u}}=-3{\bf{i}}+9{\bf{j}},~{\bf{v}}=5.8{\bf{i}}-7.1{\bf{j}}[/latex]
[latex]{\bf{u}}=6{\bf{i}}-8{\bf{j}},~{\bf{v}}=23{\bf{i}}+42{\bf{j}}[/latex]
For Problems 31–38, find the coordinate form of the vector, where
[latex]{\bf{u}}=2{\bf{i}}+3{\bf{j}},~~{\bf{v}}=-5{\bf{i}}+4{\bf{j}},~~{\bf{w}}=-2{\bf{i}}-5{\bf{j}},~~{\bf{z}}=8{\bf{i}}-3{\bf{j}}[/latex]
[latex]{\bf{u}}+{\bf{v}}[/latex]
[latex]{\bf{w}}-{\bf{z}}[/latex]
[latex]4{\bf{w}}[/latex]
[latex]-3{\bf{v}}[/latex]
[latex]2{\bf{z}}-{\bf{u}}[/latex]
[latex]-{\bf{w}}+5{\bf{u}}[/latex]
[latex]3{\bf{v}}-{\bf{w}}+2{\bf{u}}[/latex]
[latex]{\bf{z}}-2({\bf{v}}+{\bf{w}})[/latex]
For Problems 39–42, find a unit