Question 61904: Pleassse help with this question!
Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -1.
P = ( , , )
Answer by jai_kos(139)   (Show Source):
You can put this solution on YOUR website! Given the plane x + y - z = -1 ---->(1)
The line x = 1 + t, y = 2t, z = -3t ---->(2), we get
Substitue equation(2) in equation(1), we get
1 +t + 2t - (-3t) = -1
1 + 3t + 3t = - 1
1 + 6t = -1
6t = - 1 -1
6t = -2
t = -2 / 6
t = - 1/3
Now substitue the value of "t" in equation(2), we get
x = 1 + (-1/3), y = 2(-1/3), z = -3(-1/3)
x = 2 / 3 , y = -2/3 , Z = 1
Therefore the point of P(x ,y ,z) = ( 2/3 , -2/3 , 1)
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