Line Equation Calculus III Three Multiple Variable Calc Question Line Plane?

Question

Find the equation of the line passing through the point B(1,-3,0) and perpindiculat to the plane x + 2y - z = 10

Plz show me the work. I am familiar with the parametric format or x-x/x0-x = t thanks for any help

Answer 1

the normal vector of the plane is the direction vector of your line... then also... you have a point...

now, you have all you need...



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Answer 2

Find the equation of the line passing through the point
B(1,-3,0) and perpindicular to the
plane x + 2y - z = 10.

Since the line is perpendicular to the plane, the normal vector of the plane is also the directional vector of the line. And you have a point B(1, -3, 0).

The directional vector v, of the line (and normal vector of the plane) is:

v = <1, 2, -1>

Now write the equation of the line.

L(t) = B + tv
L(t) = <1, -3, 0> + t<1, 2, -1>
where t is a scalar ranging over the real numbers