Question

Find the eauation of the line perpendicular
to 5x-3y+1=0
and
passing through (4, -3)​

Answer 1

Consider the planes 5x+4y+1z=1 and 5x+1z=0

(A) Find the unique point P on the y-axis which is on both planes. (__, __, __)

(B) Find a unit vector U with positive first coordinate that is parallel to both planes. ___I + ___J + ___K

(C) Use the vectors found in parts (A) and (B) to find a vector equation for the line of intersection of the two planes, r(t) = ___I + ___J + ___K

I was able to find part A by setting x and z to 0 and solve for y:

5(0)+4y+1(0)=1

y=14=>(0,14,0)