Equations of lines and planes?

Question

Find a vector equation and parametric equations for the line.

The line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

this is only number 5 on my homework, I am screwed

help!!! this shouldnt be that hard for anyone thats taken calc 3 or linear algebra!

Answer 1

The line through the point P(1,0,6) and perpendicular to the plane x + 3y + z = 5.

Since the line is perpendicular to the plane, the directional vector v, of the line is the same as the normal vector of the plane.

v = <1, 3, 1>

To write the equation of the line all we need is a point P on the line, and the directional vector v, of the line.

L(t) = P + tv = <1, 0, 6> + t<1, 3, 1>
or
L(t) = <1 + t, 3t, 6 + t>
where t is a scalar ranging over the real numbers

The parametric form of the equation for the line is:

L(t):
x = 1 + t
y = 3t
z = 6 + t

Answer 2

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