Question

Consider the line which passes through the point P(4, 5, 2), and which is parallel to the line x=1+6t, y=2+5t, z=3+7t
find the point of intersection of this new line with each of the coordinate planes
xy-plane;(__,__,__)
xz-plane:(__,__,__)
yz-plane:(__,__,__)

Answer 1

This link could help:
http://cs.fit.edu/~wds/classes/cse5255/thesis/lineEqn/lineEqn.html

You have to have a line parallel to the set of equations therefore the slope of the line needs to be the same as the parametric equations

You develop a new set of parametric equations with the point and the slopes of 6 for x equation, 5 for y equation, and 7 for z equation

Answer 2

i know how to set up the equation but i am a bit confused on what the xy, xz, yz planes would be

Answer 3

For the xy plane -> z = 0 -> find t and then find x and y point

For the xz plane -> y = 0 -> find t and then find x and z point

For the yz plane -> x = 0 -> find t and then find y and z point