December 1, 2015

Homework Help: Vectors

Posted by Alex on Monday, April 7, 2008 at 9:49pm.

I am really lost and confused!

Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3).
a) Find their point of intersection.
b) Find a vector equation for the line perpendicular to both of the given lines that passes through their point of intersection.

For a I got the equations
3t-1u+3 = 0
2t-2u+2 = 0
t-3u+1 = 0

Then I put 2 and 3 together and got u = -4.

In the back of the book the answers says (-2, -3, 0). So am I already wrong?

2) Show that the lines r = (4,7,-1) + t(4,8,-4) and r = (1,5,4) + u(-1,2,3) intersect at right angles and find the point of intersection.

Can someone please walk me through these?

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