Find the intersection of the line r = (4,2,0) + t(0,1,-5) and the plane 7x-4y+z+7=0

Question

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Answer 1

Parametric equation of line: x = 4, y = 2 + t, z = - 5t. Substitude in equation of plane to get t for point of intersaction: 7·4 - 4(2 + t) + (- 5t) + 7 = 0, 28 - 8 - 4t - 5t + 7 = 0, 27 = 9t, t = 3. So x = 4, y = 2 + 3 = 5 and z = - - 5·3 = - 15. Point of intersaction is (4, 5, - 15).