The line r= (-8,-6,-1) + s(2,2,1), intersects the xz- and yz-coordinate planes at the points A and B, respectively. Determine the length of line segment AB.

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The line r= (-8,-6,-1) + s(2,2,1) intersects the xz and yz coordinate planes at the point A and B.

As r= (-8,-6,-1) + s(2,2,1) intersects the xz plane at A, we have y=0

At A, -6 + 2s = 0

=> s = 3

The point A is (-2, 0, 2)

As r= (-8,-6,-1) + s(2,2,1) intersects the yz plane at B, we have x=0

At B, -8 + 2s = 0

=> s = 4

The point B is (0, 2, 3)

The distance between A and B is sqrt[(-2 - 0)^2 + (0 - 2)^2 + (2 - 3)^2]

=> sqrt[4 + 4 + 1]

=> sqrt 9

=> 3

The required length of the line segment AB = 3.

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