A. find symmetric equations for the line that passes through the point (4, −4, 8) and is parallel to the vector −1, 4, −3b. find the points in which the required line in part (a) intersects the coordinate planes. i. point of intersection with xy-planeii. point of intersection with yz-planeiii. point of intersection with xz-plane

The line has equation

where is any real number. is the line containing all scalar multiples of the vector (-1, 4, -3); we add (4, -4, 8) to shift the line so that it passes through this point while remaining parallel to the the line.

To get the symmetric form, we have

Solving for in each equation gives the symmetric form,

The line has intercepts in the coordinate planes wherever either the , , or coordinate is 0.

-plane:

-plane:

-plane:

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