Question on vectors HELP!?

The points A, B and C have coordinates (3, -1, 5), (7, 1, 3) and (-5, 9, -1) respectively.





a)if L is the midpoint is AB and M is the midpoint of BC, find vectors L--%26gt;A, B--%26gt;M and L--%26gt;M





b) Find the angle between L--%26gt;M and A--%26gt;B





btw the arrow inbetween the letters eg. L--%26gt;M is meant to be above the letts, however i cannot do that here...


Could you also include your working out because i have no idea how to do this. Thanks

Question on vectors HELP!?
A, B and C have coordinates (3, -1, 5), (7, 1, 3) and (-5, 9, -1)





coordinates of L = (A + B)/2= [(7+3)/2,(1-1)/2,(5+3)/2]


=%26gt; L = (5,0,4)


similarly, M = (1,5,1)





LA = OA - OL where O is origin located at (0,0,0)


LA = (3-5)i + (-1-0)j + (5-4)k = -2i-j+k


similarly, BM = -6i+4j-2k


and LM = -4i+5j-3k


LM DOT PRODUCT AB = modulous(LM)*modulous(AB)*COS(THETA), where theta is the angle between vectors LM %26amp; AB.


AB = 4i+2j-2k


LM DOT AB = -4*4+5*2-3*-2 = -16+10+6 = 0


cos(theta) = 0 =%26gt; theta = 90degrees


vectors are perpendicular to each other!!!
Reply:oooh man vectors are a bi*ch.....i hated trig