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August 11th, 2011, 09:07 AM  #1 
Newbie Joined: Jul 2011 Posts: 3 Thanks: 0  Help with vector question please!!!!1
Show that the lines (x5)/4 = (y7)/4 = (z+3)/5 and (x/7 = y4 = (z5)/3 intersect at a point and find their point of intersection. 
August 11th, 2011, 03:36 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Help with vector question please!!!!1
The problem is easier to handle if the equations are written in parametric form. The first line: x=5+4t, y=7+4t, z=35t The second line: x=8+7s, y=4+s, z=5+3s Find s and t by equating two of the coordinates of the lines: 5+4t=8+7s (x), 7+4t=4+s (y). Once you get s and t, plug them into the formulas for the third variable (z) and hope they come out the same. If not, either you made a mistake or the lines don't meet. 

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