Point of Intersection of Line & Plane: Parametric Eqns.

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Homework Statement


Find the coordinates of the point where the line (x+1)/7 = (y-1)/-4 = (z-5)/-5 intersects the plane 3x + 3y + 2z = 5


Homework Equations


none


The Attempt at a Solution


parameterized the equation of the line to
x = -1 + 7t
y = 1 - 4t
z = 5 - 5t
 
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dracolnyte said:
parameterized the equation of the line to
x = -1 + 7t
y = 1 - 4t
z = 5 - 5t

Find the value of t which satisfies the equation of the plane 3x+3y+2z=5
 
Oh thanks a lot! I completely forgot how to do algebra since gr.12.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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