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Thread: Find the point at which the line intersects the given plane

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    Find the point at which the line intersects the given plane

    Find the point at which the line intersects the given plane.

    Line: x = y - 1 = 2z
    Plane: 4x - y + 3z = 8

    I understand how to use the cross product, dot product, and find intercepts. This problem is in section 13.5 #45 of the James Stewart Calculus book. I understand the idea but need some help in solving the problem. Thanks!
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    Quote Originally Posted by jdj333 View Post
    Find the point at which the line intersects the given plane.

    Line: x = y - 1 = 2z
    Plane: 4x - y + 3z = 8

    I understand how to use the cross product, dot product, and find intercepts. This problem is in section 13.5 #45 of the James Stewart Calculus book. I understand the idea but need some help in solving the problem. Thanks!
    The equation of the line tells you that x = 2z and y = 2z + 1. Substitute those expressions for x and y into the equation of the plane, and you have a simple equation for z.
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