Is the Vector Parametric Equation for Line L Perpendicular to Plane P?

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Homework Statement


Find the vector parametric equation of the line L passing through the point p=(1,2,3) and perpendicular to the plane P having equation 2x-3y-5z=7

Homework Equations


N/A

The Attempt at a Solution


q=P+tu

(where u is the vector of the normal)

[x,y,z]=(1,2,3)+t(2,-3,-5)

x= 1+2t
y= 2-3t
z=3-5t
 
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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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