if `axxb = bxxc != 0` with a `!= -c` then show that a+c = kb, where k is scalar.

Explanation

Given,`axxb=bxxc`
`axxb=-cxxb`
`therefore axxb+cxxb=O`
`(a+c)xxb=O`
`thereforeaxxbne O,bxxcneO,a,b,c,d "are non-zero vectors."`
`(a+c)neO`
Hence ,a+c is parallel to b.
`therefore a+c=kb (k-scalar)`
Hence proved.