1.

If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, where m is a scalar.

Answer»

Solution :`vecaxxvecb = VECBXXVECC ne VEC0`
`implies vecaxxvecb-vecbxxvecc = vec0`
`impliesvecaxxvecb+veccxxvecb = vec0[because vecbxxvecc = -veccxxvecb]`
`implies (veca+vecc)xxvecb = vec0`
`implies veca+vecc` is PARALLEL to `vecb`
`implies veca+vecc = mvecb` for some SCALAR m.(Proved)


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