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woleraymond
 3 years ago
Prove that the vectors u = 3i + j  2k , v = i + 3j+ 4k and w = 4i  2j  6k can form the sides of a triangle
woleraymond
 3 years ago
Prove that the vectors u = 3i + j  2k , v = i + 3j+ 4k and w = 4i  2j  6k can form the sides of a triangle

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imron07
 3 years ago
Best ResponseYou've already chosen the best response.1You learn linear algebra?

imron07
 3 years ago
Best ResponseYou've already chosen the best response.1Prove: 1) Try w+v, its equal u. Isn't that suspicious? This proves that these three vectors are side of a triangle. But wait! we don't know if they are in the same plane yet :) 2) To prove all of them are in the same plane, find determinant of the 3x3 matrix. If it is zero, then you got your answer.

woleraymond
 3 years ago
Best ResponseYou've already chosen the best response.0@imron07 the determinant of the 3 by 3 matrix is also zero...how does that make them to be in the same plane?

imron07
 3 years ago
Best ResponseYou've already chosen the best response.1This means one of the the three vectors aren't independent (or span new dimension) from the other two. In other word, you can make one of them by combyning the other two. Say: a*v+b*w=u You can find that a=b=1. Well, the second step isn't really neccesary actually (because by guessing, you already know that v+w=u).
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