Can Someone Verify My Calc 3 Practice Exam Solutions?

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Calc 3 exam tomorrow! Check my solutions please!

Takeing a practice exam but don't have the solutions, anyone who could verify my solutions would be appriciated!

First problem

Find the scalar equation of the plane that passes through (2,-1,0) and is perpendicular to the line x=1-t, y=2+t, z=5

My solution
-x+y= -3

Second problem

Find the scalar equation of the plane that passes through the origin and is parallel to the plane x+2y-3z=4

My solution
x+2y-3z=0

More problems to follow. Thanks in advance for any help!
 
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both look good to me
 


sweet thanks!
 

Thread 'Finding the nth roots of a complex number'

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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