# Maths-Vectors Assistance PLZZ!

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

1. 👍 0
2. 👎 0
3. 👁 136

## Similar Questions

1. ### math

Prove with vectors that for every triangle the lenght of one side is smaller than the sum of the other two sides.

asked by rara on September 23, 2012
2. ### Math;);)

Use the vector form of the Law of Cosines to show that |u + v|^2 ≤ (|u| + |v|)^2 holds for any vectors u and v. What does this prove?

asked by anonymous on January 11, 2017
3. ### Math

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

asked by Tess on April 18, 2008

prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a

asked by parth on September 22, 2009
5. ### Science

Two equal vectors are working at a point.The resultant is equal to one of those vectors.Prove that the resultant bisects the angle between the vectors.

asked by Julekha on March 14, 2016
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 G

asked by Jat on February 12, 2012
7. ### 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

asked by Jat on February 12, 2012
8. ### maths

Let V be the set of vectors (2x-3y, x+2y, -y, 4x) with x,y elements of 2 dimensional space. Addition and scalar multiplication are defined in the same way as on vectors. Prove that V is a vector space. Also, point out a basis of

asked by Buma on December 19, 2018
9. ### Linear Algebra

Prove that If a vector space is of dimension n and a set of vectors spans V, then that set of vectors must be linearly independent.

asked by John on February 26, 2013
10. ### linear algebra

Which of the given subsets of R3 are subspaces? (a) The set of all vectors of the form [a;b;0] b)The set of all vectors of the form [a;b;c] where a > 0. c) The set of all vectors of the form [a;c;c] d) The set of all vectors of

asked by kirsten on February 23, 2015

More Similar Questions