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Given initial point $\text{\hspace{0.17em}}{P}_{1}=\left(2,1\right)\text{\hspace{0.17em}}$ and terminal point $\text{\hspace{0.17em}}{P}_{2}=\left(-1,2\right),\text{\hspace{0.17em}}$ write the vector $\text{\hspace{0.17em}}v\text{\hspace{0.17em}}$ in terms of $\text{\hspace{0.17em}}i\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}j,\text{\hspace{0.17em}}$ then draw the vector on the graph.
Given initial point $\text{\hspace{0.17em}}{P}_{1}=\left(4,-1\right)\text{\hspace{0.17em}}$ and terminal point $\text{\hspace{0.17em}}{P}_{2}=\left(-3,2\right),\text{\hspace{0.17em}}$ write the vector $\text{\hspace{0.17em}}v\text{\hspace{0.17em}}$ in terms of $\text{\hspace{0.17em}}i\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}j.\text{\hspace{0.17em}}$ Draw the points and the vector on the graph.
$v=-7i+3j$
Given initial point $\text{\hspace{0.17em}}{P}_{1}=\left(3,3\right)\text{\hspace{0.17em}}$ and terminal point $\text{\hspace{0.17em}}{P}_{2}=\left(-3,3\right),\text{\hspace{0.17em}}$ write the vector $\text{\hspace{0.17em}}v\text{\hspace{0.17em}}$ in terms of $\text{\hspace{0.17em}}i\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}j.\text{\hspace{0.17em}}$ Draw the points and the vector on the graph.
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.
$\left|v\right|=8,\theta =\mathrm{220\xb0}$
$\left|v\right|=5,\theta =\mathrm{135\xb0}$
A 60-pound box is resting on a ramp that is inclined 12°. Rounding to the nearest tenth,
a. 58.7; b. 12.5
A 25-pound box is resting on a ramp that is inclined 8°. Rounding to the nearest tenth,
Find the magnitude of the horizontal and vertical components of a vector with magnitude 8 pounds pointed in a direction of 27° above the horizontal. Round to the nearest hundredth.
$x=7.13\text{\hspace{0.17em}}$ pounds, $\text{\hspace{0.17em}}y=3.63\text{\hspace{0.17em}}$ pounds
Find the magnitude of the horizontal and vertical components of the vector with magnitude 4 pounds pointed in a direction of 127° above the horizontal. Round to the nearest hundredth.
Find the magnitude of the horizontal and vertical components of a vector with magnitude 5 pounds pointed in a direction of 55° above the horizontal. Round to the nearest hundredth.
$x=2.87\text{\hspace{0.17em}}$ pounds, $\text{\hspace{0.17em}}y=4.10\text{\hspace{0.17em}}$ pounds
Find the magnitude of the horizontal and vertical components of the vector with magnitude 1 pound pointed in a direction of 8° above the horizontal. Round to the nearest hundredth.
A woman leaves home and walks 3 miles west, then 2 miles southwest. How far from home is she, and in what direction must she walk to head directly home?
4.635 miles, 17.764° N of E
A boat leaves the marina and sails 6 miles north, then 2 miles northeast. How far from the marina is the boat, and in what direction must it sail to head directly back to the marina?
A man starts walking from home and walks 4 miles east, 2 miles southeast, 5 miles south, 4 miles southwest, and 2 miles east. How far has he walked? If he walked straight home, how far would he have to walk?
17 miles. 10.318 miles
A woman starts walking from home and walks 4 miles east, 7 miles southeast, 6 miles south, 5 miles southwest, and 3 miles east. How far has she walked? If she walked straight home, how far would she have to walk?
A man starts walking from home and walks 3 miles at 20° north of west, then 5 miles at 10° west of south, then 4 miles at 15° north of east. If he walked straight home, how far would he have to the walk, and in what direction?
Distance: 2.868. Direction: 86.474° North of West, or 3.526° West of North
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