Find the point at which the line intersects the given plane. x = 3 - t, y = 2 +

Rivka Thorpe

Rivka Thorpe

Answered question

2021-10-17

Find the point at which the line intersects the given plane. x=3t, y=2+t, z=5t; xy+2z=9

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-10-18Added 93 answers

Substitute the parametric equations of the line into the equation of the plane, we obtaint
3t(2+t)+25t=9
3t2t+10t=9
8t=8
t=1 ()
Putting () in the parametric equation, we get the cootdinates of the point of intersection the line and the plane.
x=31
=2
y=2+1
=3
z=51
=5

So, the point of intersection is
P(2,3,5)
Result
P(2,3,5)

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