Posted by **Babanla** on Monday, April 16, 2007 at 8:05am.

Prove that the vectors u=3i+j-2k ,

v= -i+3j=4k, and w=4i-2j-6k 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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