Consider the plane $\vec { r } ( s , t ) = ( - 4 + s - 4 t ) \vec { i } + ( 5 - s + 4 t ) \vec { j } + ( 6 - 4 t - s ) \vec { k }$ Does it contain the point (-7, 8, -7)?

Question

Quizplus · Accepted Answer

To check if the point (-7, 8, -7) lies on the plane, solve the system of equations: -4 + s - 4t = -7, 5 - s + 4t = 8, and 6 - 4t - s = -7. Solving these gives s = 2 and t = 1, which satisfies all equations, confirming the point lies on the plane.

Consider the Plane r⃗(s,t)=(−4+s−4t)i⃗+(5−s+4t)j⃗+(6−4t−s)k⃗\vec { r } ( s , t ) = ( - 4 + s - 4 t ) \vec { i } + ( 5 - s + 4 t ) \vec { j } + ( 6 - 4 t - s ) \vec { k }r(s,t)=(−4+s−4t)i+(5−s+4t)j​+(6−4t−s)k

Consider the Plane $\vec { r } ( s , t ) = ( - 4 + s - 4 t ) \vec { i } + ( 5 - s + 4 t ) \vec { j } + ( 6 - 4 t - s ) \vec { k }$