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, veca-9vecb-vecc,3veca+2vecb-vecc where 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

Check whether the following sets of three points are collinear: -2veca+3vecb+5vecc, veca+2vecb+3vecc, 6veca-vecc

Examine whather followig vectors are coplanar or not: 5veca +6vecb + 7vecc, 7veca - 8vecb + 9vecc, 3veca + 20 vecb + 5vecc

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: 4veca+5vecb+vecc,-vecb-vecc, 3veca+9vecb+4vecc,-4veca+4vecb+4vecc

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

If veca,vecb,vecc are non coplanar vectors, check whether the following points are coplanar: 6veca+2vecb-vecc, 2veca+vecb+3vecc, -veca+2vecb-4vecc, -12veca-vecb-3vecc

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

If veca, vecb, vecc , be three on zero non coplanar vectors estabish a linear relation between the vectors: 8vecb+6vecc, veca+vecb+vecc, 2veca-vecb+vecc, veca-vecb-vecc