Q4 (8 points) (a) Find parametric equations to the line passing through the point A(5,-2,9) and...

Question

Question

math algebra

Answer 1

Answer #1

A vector perpendicular to the plane ax+by+cz+d=0
is given by 〈a,b,c〉.

So a vector perpendicular to the plane 3x - y - 6z + 2 = 0
is 〈3,-1,-6〉

The parametric equation of a line through (x0,y0,z0)
and parallel to the vector 〈a,b,c〉 is
x=x0+ta
y=y0+tb
z=z0+tb

So the parametric equation of our line is
x=5+3t
y=-2−t
z=9-6t

The vector form of the line is →r=〈5,-2,9〉+t〈3,-1,-6〉

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Answer 2

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