Question

Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)

Answer 1

Substituting this coordinates in the equation of plane

(-48 – 6 – 36) + (-24 – 18+ 24) = 5

$-18t = 95, t = \frac{-95}{18}$

Hence the point of intersection will be given by substituting t=-95/18 in these points

$x = -6 + \frac{95}{6} = \frac{59}{6}$

$y = -3 + \frac{95}{2} = 89/2$

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