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 and vecc` are three non-zero, non-coplanar vectors,then

1.	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`.
Answer» Any vector `vecr` can be uniquely expressed as a linear combinatioin of three non-coplanar vectors. Let us choose that `" "7veca -11 vecb + 15 vecc= x(veca-2vecb+ 3vecc) + y (2veca-3vecb+4vecc)+ z(3veca-4vecb+5vecc)` Comparing the coefficients of `veca, vecb and vecc` on both sides, we get `x+2y+3z=7, -2x-3y-4z=-11, 3x+4y+ 5z=15` Eliminating x and then solving for `y and z`, we get x=1, y=3, z=0`

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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`.

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