How do you find the parametric equations for the line through the point P = (4, -4, 1) that is perpendicular to the plane 3x + 1y - 4z = 1?

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Answer 1 · 2017-02-04T18:41:22

#x=4+3t, y=-4+t, z=1-4t, t in RR.#

Since the reqd. line is #bot# to the plane #: 3x+y-4z=1#, the

direction vector #vecl# of the line is #||# to the normal

#vecn# of the plane,

Here, #vecn=(3,1,-4)#, and, we take #vecl=vecn#.

Now, the Parametric Eqn. of a line through a pt.#(x_1,y_1,z_1)#

and having direction vector #vecl=(l_1,l_2,l_3)# is given by,

#(x,y,z)=(x_1,y_1,z_1)+t(l_1,l_2,l_3), t in RR#.

# :. (x,y,z)=(4,-4,1)+t(3,1,-4), t in RR,# or,

#x=4+3t, y=-4+t, z=1-4t, t in RR.#