Chapter Questions
Draw a vector $\mathbf{s}$ to represent a wind blowing south at 100 miles per hour for one hour and a vector p representing a plane traveling east that has gone 300 miles.
Draw a vector representing a weight of 230 pounds.
Draw the resultant of vectors $\overrightarrow{A B}$ and $\overrightarrow{C D}$ as shown in the following figure.(Figure can't copy)
Draw the resultant of vectors v and u as shown in the following figure.(Figure can't copy)
Draw the resultant of vectors u and v as shown in the following figure.(Figure can't copy)
Solve the parallelogram of forces in the following figure.(Figure can't copy)
A force of $14 \mathrm{lbs}$. and a force of $12 \mathrm{lbs}$. are acting on a body at an angle of $90^{\circ}$. What are the magnitude and angle of the resultant with respect to the $14 \mathrm{lb}$. force?
An airplane is trying to fly due west at $600 \mathrm{mph}$. Because of a wind from the north, the plane's actual path is $10^{\circ}$ south of west. Assuming the wind to be blowing at a steady pace, what is its magnitude to the nearest whole $\mathrm{mph}$ ?
What is the magnitude of the speed of the plane in Problem 8?
If the endpoints of vector $\overrightarrow{A B}$ are $A(-3,-7)$ and $B(2,5)$, what are the coordinates of standard vector $\overrightarrow{O P}$ if $\overrightarrow{O P}=\overrightarrow{A B}$ ?
If the endpoints of vector $\overrightarrow{C D}$ are $C(-6,-9)$ and $D(2,4)$, what are the coordinates of standard vector $\overrightarrow{O M}$ if $\overrightarrow{O M}=\overrightarrow{C D}$ ?
If the endpoints of vector $\overrightarrow{A B}$ are $A(3,6)$ and $B(13,14)$, what are the coordinates of standard vector $\overrightarrow{O P}$ if $\overrightarrow{O P}=\overrightarrow{A B}$ ?
Refer to the preceding figure as the model for Problems 13-16.(Figure can't copy)Find the rectangular components of the vector $30 \angle 30^{\circ}$ to the nearest integer.
Refer to the preceding figure as the model for Problems 13-16.(Figure can't copy)The rate and angle with the river bank of a boat crossing a stream in miles per hour is $20 \angle 70^{\circ}$. What are the cross stream and current components of the boat's velocity?
Refer to the preceding figure as the model for Problems 13-16.(Figure can't copy)The vertical component of a force is four times the magnitude of the horizontal component. Find the angle the resultant force makes with the smaller component.
Find the rectangular components of the vector $30 \angle 45^{\circ}$ (answer may be left in radical form).
Find the magnitude of vector $\mathbf{h}=(-5,9)$
Vector $\mathbf{b}=(6,-9)$; vector $\mathbf{c}=(p, q)$; $\mathbf{b}=\mathbf{c}$. Find the value of $p$.
Find the magnitude of vector $\mathbf{m}=(-12,-16)$
Multiply $\mathbf{v}(-8,9)$ by 10.
If $\mathbf{r}=(m, n)$ and $\mathbf{s}=(p, q)$, find the product of 9 and $\mathbf{r}+\mathbf{s}$.
If $\mathbf{m}=(7,-8)$ and $\mathbf{n}=(6,-9)$, find the product of -7 and $\mathbf{m}-\mathbf{n}$.
Multiply $\mathbf{v}(5,-4)$ by $\mathbf{u}(-8,7)$.
If $\mathbf{r}=(c, d)$ and $\mathbf{s}=(a, b)$, find the product $\mathbf{r} \cdot \mathbf{s}$.
If $\mathbf{p}=(5,-8)$ and $\mathbf{q}=(-7,9)$, find the dot product of $\mathbf{p}$ and $\mathbf{q}$.