Find the intersection.
-x = -2 + 2t, y = 1 + 10t, z = -2 + 7t ; -10x + 2y + 8z = 4
A) $\left( - \frac { 29 } { 14 } , \frac { 9 } { 14 } , - \frac { 9 } { 4 } \right)$
B) $( 0,11,5 )$
C) $\left( - \frac { 27 } { 14 } , \frac { 19 } { 14 } , \frac { 5 } { 4 } \right)$
D) $( - 4 , - 9 , - 9 )$

Question

Find the intersection.
-x = -2 + 2t, y = 1 + 10t, z = -2 + 7t ; -10x + 2y + 8z = 4 
A) $\left( - \frac { 29 } { 14 } , \frac { 9 } { 14 } , - \frac { 9 } { 4 } \right)$
B) $( 0,11,5 )$
C) $\left( - \frac { 27 } { 14 } , \frac { 19 } { 14 } , \frac { 5 } { 4 } \right)$
D) $( - 4 , - 9 , - 9 )$

Quizplus · Accepted Answer

Substitute $x = -2 + 2t$, $y = 1 + 10t$, and $z = -2 + 7t$ into the equation $-10x + 2y + 8z = 4$. Solve for $t$ and then substitute back to find the intersection point, which matches option A.

Find the Intersection (−2914,914,−94)\left( - \frac { 29 } { 14 } , \frac { 9 } { 14 } , - \frac { 9 } { 4 } \right)(−1429​,149​,−49​)

Find the Intersection $\left( - \frac { 29 } { 14 } , \frac { 9 } { 14 } , - \frac { 9 } { 4 } \right)$