- #1
knowLittle
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Homework Statement
Find parametric equations for the line which passes through the point (1; 2; 3)
and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 -2x.
I have seen the result for this problem, but it's different than mine. I'm not sure, what I'm doing wrong. Please, help.
The Attempt at a Solution
If the line is parallel to two planes, then the line must be orthogonal to both planes' normals.
First, I notice that the planes' normal are:
n1=(3,1,5) and n2=(2,0,1)
Then, the direction vector of the line is p=<a,b,c>
and since, the vector and the normals are orthogonal.
*Dot Products*
p.n1=0
p.n2=0
I get :
3a+b+5c=0
2a+0+c=0
Using determinants, I find that the direction of the line is: 1i+7j-2k
{x-x_{1}} over {1} ={y-y_{1}} over {7} ={z-z_{1}} over {-2} =t
or
(x-1)=(y+2)/7 =(z-3)/-2 =t ...where the values of the point passed are plugged in on the numerator.
So, my parametric equation yields:
x=t+1
y=7t-2
z=-2t+3