Answer:
• (x, y, z) = (3+t, 1-t, 8+4t) . . . equation of the line
• xy-intercept (1, 3, 0)
• yz-intercept (0, 4, -4)
• xz-intercept (4, 0, 12)
Step-by-step explanation:
The line's direction vector is given by the coordinates of the plane: (1, -1, 4). So, the parametric equations can be ...
(x, y, z) = (3, 1, 8) + t(1, -1, 4) . . . . . parametric equation for the line
or
(x, y, z) = (3+t, 1-t, 8+4t)
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The various intercepts can be found by setting the respective variables to zero:
xy-plane: z=0, so t=-2. (x, y, z) = (1, 3, 0)
yz-plane: x=0, so t=-3. (x, y, z) = (0, 4, -4)
xz-plane: y=0, so t=1. (x, y, z) = (4, 0, 12)
