Homework SourseConsider the line which passes through the point P3 5 3 and
Consider the line which passes through the point P(3, 5, -3), and which is parallel to the line x=1+5t,y=2+4t,z=3+3t
Find the point of intersection of this new line with each of the coordinate planes:
xy-plane:
xz-plane:
yz-plane:
Find the point of intersection of this new line with each of the coordinate planes:
xy-plane:
xz-plane:
yz-plane:
Solution
line is parallel to given line and passes through the point P. hence its equation must be x = 3+5t ; y= 5+4t ; z=-3+3t now xy plane z=0 hence 0 = -3 + 3t t = 1 hence x = 8 y = 9 hence point is (8,9,0) xz plane y=0 hence 5+4t=0 t = -5/4 hence x = -13/4 and z = -27/4 hence point is (-13/4 , 0 , -27/4 ) yz plane x=0 hence 3+5t =0 hence t = -3/5 y= -13/5 and z= -24/5 hebce point is (0,-13/5,-24/5)
