Question

determine whether or not u and r are linearly dependent where u=(2,4,-8) , r=(3,6,-12)​

Answer 1

Answer:

let ou=2i+4j_8k

or=3i+6j-12k

here I,j,k are unit vector in x,y,z direction respectively

condition for linear dependency is,

ou=k×or

here k is some constant

k can take any real value excluding o

2(i+2j+-4k)=3(i+2j-4ķ)

(i+2j+4k)=3/2(i+2j-4k)

k=3/2

hence it is proved that both u and v are linearly dependent