Examine whether the following vectors from a linearly dependent or independent set of vector: `veca(1,-2,30,vecb=(-2,3,-4),vecc=(1,-1,5)``

Examine whether the following vectors from a linearly dependent or independent set of vector: veca-3vecb+2vecc, vec-9vecb-vecc,3a+2vecb-vecc whre veca,vecb,vecc are non zero non coplanar vectors

Examine whether the following vectors from a linearly dependent or independent set of vector: hati+3hatj+5hatk, 2hati+6hatj+10hatk

examine whether the following sets of vectors are lineerly dependent S:{(1,-3,2),(2,-1,1),(1,7,4)

Examine whather followig vectors are coplanar or nto: veca+vecb-vecc, veca-3vecb+vecc nd 2veca-vecb-vecc

If veca, vecb and vecc are three non-zero, non-coplanar vectors,then find the linear relation between the following four vectors : veca-2vecb+3vecc, 2veca-3vecb+4vecc, 3veca-4vecb+ 5vecc, 7veca-11vecb+15vecc .

If veca, vecb, vecc , be three on zero non coplanar vectors estabish a linear relation between the vectors: veca+3vecb=3vecc, veca-2vecb+3vecc, vec+5vecb-2vecc,6veca=14vecb+4vecc

If veca, vecb, vecc are non-coplanar vectors, prove that the following vectors are coplanar. (i) 3veca - vecb - 4vecc, 3veca - 2vecb + vecc, veca + vecb + 2vecc (ii) 5veca +6vecb + 7vecc, 7veca - 8vecb + 9vecc, 3veca + 20 vecb + 5vecc

If a,b,c are linearly independent, then ([[veca+2vecb,2vecb+vecc,5vecc+veca] ])/([vecavecbvecc])

If vec a,vec b,vec c are linearly independent vectors then which one of the following set of vectors is linearly dependent?

If veca,vecb and vecc are three vectors of which every pair is non colinear. If the vector veca+vecb and vecb+vecc are collinear with the vector vecc and veca respectively then which one of the following is correct? (A) veca+vecb+vecc is a nul vector (B) veca+vecb+vecc is a unit vector (C) veca+vecb+vecc is a vector of magnitude 2 units (D) veca+vecb+vecc is a vector of magnitude 3 units