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

Question

psymon · Answer

Think you could give that to me in parametric form first? :P

anonymous · Answer

$$x=-8+2s$$
$$y=-6+2s$$
$$z=-1+s$$

then?

psymon · Answer

Right, so it interesects the xz plane, meaning its where y = 0. So solve for your time when y = = and see what the correspnding x and z coordinates would be :P

anonymous · Answer

can you please elaborate more???:)

psymon · Answer

Yeah, sure. 

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So what I have shaded is the xz plane. So when the line is intersecting with this xz plane, it means y has to be 0. Well, y is zero at some time s. But at that same time s, we can find what the x and z coordinates are. When we find those x and z coordinates, we'll know the point that the line intersects with the xz plane.