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Find the​ point, P, at which the line intersects the plane. x equals negative 3 minus 8 tx=−3−8t​, y equals negative 6 plus 5 ty=−6+5t​, z equals negative 6 minus 6 tz=−6−6t​; negative 7 x plus 2 y plus 8 z equals negative 4−7x+2y+8z=−4 The​ point, P, at which the line intersects the plane is left parenthesis nothing comma nothing comma nothing right parenthesis,,. ​(Simplify your answer. Type an ordered​ triple.)

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sqdancefan

Answer:

  P = (-18 5/9, 3 13/18, -17 2/3)

Step-by-step explanation:

The given point must satisfy both the equation of the line and that of the plane. We can substitute for x, y, and z in the plane's equation to get ...

  -7(-3-8t) +2(-6+5t) +8(-6-6t) = -4

  21 +56t -12 +10t -48 -48t = -4

  18t -39 = -4 . . . collect terms

  18t = 35 . . . . . . add 39

  t = 35/18 . . . . . .divide by the coefficient of t

The point is ...

  (x, y, z) = (-3-8(35/18), -6+5(35/18), -6-6(35/18))

  P = (x, y, z) = (-18 5/9, 3 13/18, -17 2/3)

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