Determine whether the vectors lie in a plane, and if so, whether they lie on a line. (a) $\mathbf{v}_{1}=(1,2,1), \mathbf{v}_{2}=(-7,1,3), \mathbf{v}_{3}=(-14,-1,-4)$ (b) $\mathbf{v}_{1}=(2,1,-1), \mathbf{v}_{2}=(1,3,4), \mathbf{v}_{3}=(1,1,0)$ (c) $\mathbf{v}_{1}=(6,-4,8), \mathbf{v}_{2}=(-3,2,-4), \mathbf{v}_{3}=(9,-6,-12)$.

Do the points A ( - 2 , - 1 ) , B ( 1, 5 ) , and C ( 4, 11 ) lie on the same line? Without using a graph, how do you know?

Do the points in the set lie on the same line? Explain your answer. D(-2, 3), E(0, -1), F(2, 1)

Complete with always, sometimes, or never to make each statement true.

Two lines that lie in parallel planes are $\underline{\quad?\quad}$ parallel.

Describe a real-life example of three lines in space that do not intersect each other and no two of which lie in the same plane.

Points $A, B$, and $C$ lie on $\odot O$.

$\overleftrightarrow{C D}$ intersects $\odot O$ in one point. $\overleftrightarrow{C D}$ is called a _____ ?

Plot the points and find the distance between them. State whether the points lie on a horizontal or a vertical line. $(-120,-2),(130,-2)$

If the points $\left(2, y_1\right)$ and $\left(-2, y_2\right)$ lie on the graph of $y=a x^2+b x+c$, and $y_1-y_2=-8$, find the value of $b$.

State an equation that models the situation. Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300 and a TV ad costs$ 700. He has $ 7,500 to spend on the ads.

Find the area of the triangle whose sides lie on the graphs of 3x+y+1=0, x+4y-7=0, and -5x+2y+13=0.

In each part, determine whether the three vectors lie on the same line in $R^3$.

$v_1$ = (2,-1,4), $v_2$ = (4,2,3), $v_3$=(2,7,-6)

Determine whether the points

$$P_1,P_2$$

and

$$P_3$$

lie on the same line.

$$P _ { 1 } ( 1,0,1 ) , P _ { 2 } ( 3 , - 4 , - 3 ) , P _ { 3 } ( 4 , - 6 , - 5 )$$

Determine whether (0, -7),

$$\left( - 6 , - \frac { 5 } { 3 } \right)$$

, and (-2, -3) lie on the graph of each function.

$$x ^ { 2 } - y = 7$$

Use what you know about the Vocabulary words to answer the question below.

Why does it take audacity to vehemently deny that you told a lie?