(a) Find symmetric equations for the line that passes through the point and is p

Question

(a) Find symmetric equations for the line that passes through the point

and is parallel to the vector

(b) Find the points in which the required line in part (a) intersects the coordinate planes.
point of intersection with xy-plane     

point of intersection with yz-plane     

point of intersection with xz-plane     

Find symmetric equations for the line that passes through the point (2, ?5, 9) and is parallel to the vector Find the points in which the required line in part (a) intersects the coordinate planes.point of intersection with xy-plane

Explanation / Answer

a) symmetric equations through (2, -5, 9) and parallel to vector <-1, 4, -3>

From part a, you get the symmetric equations for the line:

(x - 2) / (-1) = (y + 5) / 4 = (z - 9) / (-3)

You can also write parametric equations for the line:

x = x0 + at

y = y0 + bt

z = z0 + ct

x = 2 - t

y = -5 + 4t

z = 9 - 3t

b) intersection with xy plane means z = 0:

z = 0 gives 9 - 3t = 0 or t = 3

Then x = 2 - 3 = -1

y = -5 + 4(3) = 7

(-1, 7, 0)

intersection with yz plane means x = 0:

x = 0 gives 2 - t = 0 or t = 2

y = -5 + 4(2) = 3

z = 9 - 3(2) = 3

(0, 3, 3)

intersection with xz plane means y = 0:

y = 0 gives -5 + 4t = 0 or t = 5/4

x = 2 - 5/4 = 3/4

z = 9 - 3(5/4) = 21/4

(3/4, 0, 21/4)

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