MathsVectors Assistance PLZZ!
posted by Babanla .
Prove that the vectors u=3i+j2k ,
v= i+3j=4k, and w=4i2j6k can form the sides of a triangle
They will form a triangle if they are linearly dependent, that is, if
(3,1,2)= m(1,3,4) + n(4,2,6)
from which we get 3 equations in two unknowns.
m + 4n = 3 #1
3m  2n = 1 #2
4m  6n = 2 #3
let's solve #1 and #2
double #2 plus #1:
m + 4n = 3
6m  4n = 2

5m = 5
m=1
back in #1, n=1
substitute those values in #3 which we have not used.
Left side = 4m  6n
=4  6
= 2
= right side
Therefore they are linearly dependent and thus can form a triangle
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