Solve the problem.
-Find the vector equation of the line through $A$ and $B$.
$$A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )$$
A) $\mathrm { r } = \langle 7,6 , - 7 \rangle - \mathrm { t } \langle 6,9,2 \rangle$
B) $\mathrm { r } = \langle 7,6 , - 7 \rangle + t \langle - 6 , - 9 , - 2 \rangle$
C) $\mathrm { r } = \langle 6,9,2 \rangle + \mathrm { t } \langle 7,6 , - 7 \rangle$
D) $r = \langle 7,6 , - 7 \rangle - t \langle - 6 , - 9 , - 2 \rangle$

Question

Quizplus · Accepted Answer

The vector equation of a line can be found using the formula $r = a + t(b - a)$, where $a$ and $b$ are points on the line, and $t$ is a scalar. Subtracting the coordinates of point $A$ from point $B$ gives the direction vector $\langle 1 - 7, -3 - 6, -9 + 7 \rangle = \langle -6, -9, -2 \rangle$. Thus, the correct equation is $r = \langle 7,6,-7 \rangle + t\langle -6,-9,-2 \rangle$.

Solve the Problem AAA And BBB A=(7,6,−7),B=(1,−3,−9),C=(6,−8,7)A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )A=(7,6,−7),B=(1,−3,−9),C=(6,−8,7)

Solve the Problem $A$ And $B$ $A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )$