A) The question is [let u and v be vectors]:
prove that ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2
and interpret the result geometrically by translating it into a theorem about parallelograms.
I went about proving the statement component wise, resulting in 2(u1)^2+2(u2)^2+ 2(v1)^2 + 2(v2)^2 = 2(u1)^2+2(u2)^2+ 2(v1)^2 + 2(v2)^2; however I don't know how to translate that into a theorem about parallelograms. Am I even attacking this problem in the correct manner?
B) Find the parametric equations for the line that is perpendicular to L1: x = 1 + 2t, y= 2-t, z=4-2t and L2: x= 9+t, y=5+3t, z = -4-t, and passes through their point of intersection
I found the point of intersection at (7, -1, -2) and I know that there is no y direction, but I cannot seem to find the x and z direction. Pretty much I need to find a and b in the following line but i do not know how.
x= 7 + At
y= -1
z= -2 + Bt
Any help on either would really be appreciated! Thanks!
2006-09-30
17:13:53
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2 answers
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asked by
Mimi
2