Question

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1, 0, 5) and perpendicular to the plane x 3y z

Answer 1

Answer:

Vector equation, ř = <1, 0, 5> + <1, 3, 1>t

The Parametric Equation is:

x = 1 + t

y = 3t

z = 5 + t

Explanation:

<a, b, c> is a vector perpendicular to the plane ax + by + cz + d = 0.

By this, a vector perpendicular to the plane

x + 3y + z = 0

is

<1, 3, 1>

The Parametric Equation of a line through the point

[tex](x_0, y_0, z_0)[\tex]

and parallel to the vector <a, b, c> is given as

[tex]x = x_0 + at[\tex]

[tex]y = y_0 + bt[\tex]

[tex]z = z_0 + ct[\tex]

So, the Parametric Equation is

x = 1 + t

y = 3t

z = 5 + t

The vector form of the line is

ř = <1, 0, 5> + <1, 3, 1>t