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NATURE.M
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Homework Statement
Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°.
L1:
x = 4 + 2t
y = 8 + 3t
z = -1 − 4t
L2:
x = 7 - 6t
y = 2+ t
z = -1 + 2t
Homework Equations
vector, parametric, symmetric equations of line in R3 and cross product equation.
The Attempt at a Solution
I obtained the direction vector for the line (L3) that intersects L1 and L2. It is [1,2,2].
And I let the point of intersection between L3 and L1 be:
[x1,y1,z1]=[4,8-1]+t[2,3,-4], tεℝ
And let the point of intersection between L3 and L2 be:
[x2,y2,z2] = [7,2,-1]+s[-6,1,2], sεℝ
And now to find the scalar multiple of direction vector of the L3 that intersects point 1 and point 2.
So, [x1,y1,z1]+n[1,2,2]=[x2, y2, z2], nεℝ
And when I solve I obtain s=-1, n=-1,..
But then I saw a different approach in which the individual used,
[x1,y1,z1]-[x2, y2, z2]=n[1,2,2], nεℝ
And this yields, s=1, n=1, t=-1.
So my question is which method is accurate/correct, or does it not really matter a great deal?