Find the intersection.
-x = -10 - 10t, y = + 4t, z = -6 + 4t ; x - 10y - 8z = -3
A) $\left( - \frac { 955 } { 76 } , \frac { 77 } { 38 } , - \frac { 189 } { 38 } \right)$
B) $( - 20,5 , - 2 )$
C) $( 0 , - 3 , - 10 )$
D) $\left( - \frac { 565 } { 76 } , - \frac { 1 } { 38 } , - \frac { 267 } { 38 } \right)$

Question

Find the intersection.
-x = -10 - 10t, y = + 4t, z = -6 + 4t ; x - 10y - 8z = -3 
A) $\left( - \frac { 955 } { 76 } , \frac { 77 } { 38 } , - \frac { 189 } { 38 } \right)$
B) $( - 20,5 , - 2 )$
C) $( 0 , - 3 , - 10 )$
D) $\left( - \frac { 565 } { 76 } , - \frac { 1 } { 38 } , - \frac { 267 } { 38 } \right)$

Quizplus · Accepted Answer

First, we plug in the parametric equations into the plane equation to get:

$$-10-10t-10y-8(-6+4t)=-3$$

Simplifying this gives:

$$t= \frac{-565}{76}$$

Now that we have the value of t, we can plug it back into the parametric equations to get the intersection point:

$$x=-10-10t=-\frac{565}{76}$$
$$y=4t=-\frac{1}{38}$$
$$z=-6+4t=-\frac{267}{38}$$

Therefore, the intersection point is:

$$\left(- \frac { 565 } { 76 } , - \frac { 1 } { 38 } , - \frac { 267 } { 38 } \right)$$

which is given by choice D.

Find the Intersection (−95576,7738,−18938)\left( - \frac { 955 } { 76 } , \frac { 77 } { 38 } , - \frac { 189 } { 38 } \right)(−76955​,3877​,−38189​)

Find the Intersection $\left( - \frac { 955 } { 76 } , \frac { 77 } { 38 } , - \frac { 189 } { 38 } \right)$