# Maths-Vectors Assistance PLZZ!

posted by .

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

## Similar Questions

1. ### math

If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors …
2. ### Maths-Vectors Help!

Please can you help me as I have just been introduced to your Help Forum: Determine whether the vectors u, v and w given below are linearly independent or dependent where u, v and w are non-colliner vectors such that u=2a-3b+c , v=3a-5b+2c …
3. ### Math

Prove that vectors u, v and w are coplanar if and only if vectors u, v and w are linearly dependent.
4. ### Math

For which real values of x do the following vectors form a linearly dependent set in R3?
5. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and G
6. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and F
7. ### linear algebra

Which of the given subsets of R3 are subspaces?
8. ### math

The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints …
9. ### Vectors - Maths

Given that a = i - j + 2k, b = i + 2j + mk and c = 3i + nj + k, are linearly dependent. Express m in terms of n in simplest fraction form. Answer: m = (2n-9)/(n+3) Can someone pls show their working and explanation?
10. ### Vectors - Maths

In triangle ABD, AC = CD = CB. Let AB = u and BC = v. Prove that DAB is a right angle triangle. AC is the midpoint of the assumed "right angle triangle" and is equidistant from the three vertices. Angle DAB is presumed to be 90. Pls …

More Similar Questions