Question

If `veca xx vecb = vecb xx vecc ne 0 ` where `veca , vecb and vecc` are coplanar vectors, then for some scalar k prove that `veca+vecc = kvecb`.

Answer 1

since `veca xx vecb = vecb xx vecc ne vec0` , we have
`veca xx vecb - vecb xx vecc = vec0`
` or veca xx vecb + vecc xx vecb = vec0`
`or ( veca + vecc) xx vecb = vec0 `
Hence, `veca + vecb` is parallel to `vecb` . Thus ,
`veca + vecc = k vecb`