If a parallelepiped with sides $\overline{DE}, \overline{DF}$, and $\overline{DG}$ has "7ero volume." what can you say about points D, E,F and $G$ ?

a. Navigation Make a diagram showing the result of sailing a ship 3 mi on a course of 040 degrees followed by sailing it 8 mi on a course of 100 degrees

b. From your diagram, estimate the distance of the ship from its starting point.

c. Find the exact distance of the ship from its starting point by using the law of cosines.

In the given exercise, give angle measures to the nearest tenth of a degree. Given A(1,5), B(4,6), and C(2,8). find the measure of angle A.

Find the angle between (8,6,0) and (2,-1,2) to the nearest tenth of a degree.

If the "area" of triangle LMN is zero, what can you conclude about points L, M, and N ?

In the given exercise, find a Cartesian equation of the plane described. Vector (2,3,5) is perpendicular to the plane that contains point A(3,1,7).

Find the coordinates of the point P described.

$A(7,-2), B(2,8) ; \frac{4}{5}$ of the way from $A$ to $B$.

Complete the following statement. The parallelogram ABCD is given. $\overrightarrow{AB}+\overrightarrow{AD}=$

Repeat previous exercise for the vectors u = (1, 2, 1) and v = (1, 1, 2).

Find the center and radius of the sphere with equation

$$x^{2}+y^{2}+z^{2}-6 x+10 y+2 z=65$$

In the given exercise, give angle measures to the nearest tenth of a degree. Find the measure of the angle between u=(1,3) and v=(-8,5).

In the given exercise, find the area of each figure, given points $P(4,3), Q(7,-1)$, $R(2,3), S(-3,6), T(-5,4)$, and $V(-2,-5)$. $\square$ with sides $\overline{PS}, \overline{PI}$

A line has parametric equations x=5-t and y=4+21. Give a vector equation and a Cartesian equation of the line.

On graph paper, make a vector diagram showing a motorboat heading cast at 10 knots. Add to your diagram a vector representing a current moving southeast. Show the boat's resultant velocity if the current moves at:

(a) 2 knots,

(b) 3 knots, and

(c) 4 knots.