Calc III, Determing the coordinates of P

mr_coffee

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Sep 12, 2005
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Hello everyone. I'm stuck on the last part of this problem. It says, Draw two distinct nonzero postion vectors a = <x1,y1> and b = <x2,y2> such that the angle between them is less than pi/2. Draw the line L perpendicular with the line determined by the bector a such that l passes through the terminal point of b. Let P = (s,t) be the point where L intersects a. Determine the length of the line segment connecting the origin to the point P. Determine the coordinates of P. I drew a picture and I found the L = mx+b. The line determined by a = y1/x1 * x. m = -x1/y1 through (x2,y2). So now I have 2 lines, I need to find the intercept of these 2 lines to determine the coordinates of P (s,t). Any ideas on how i can do this? Thanks. I'm confused on what my 2 lines are exactly. Here is a picture, don't look at the left part, that is incorrect but the drawing itself is right. Picture:
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I fear that you may have confused yourself with the diagrams.
You really just want the length of the projection of b onto a.
Note that ΔOPB is a right triangle, b is its hypotenuse.
If Θ is the angle between a& b, then ||OP||=||b||cos(Θ)=||b||(ab)/[ ||a|| ||b||].
 
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