If ` vec axx vec b= vec bxx vec c!=0,\ ` then show that ` vec a+ vec c=m vec b ,\ w h e r e\ m` is any scalar.

Explanation

`vec{a} times vec{b}=vec{b} times vec{c} `

`Rightarrow vec{a} times vec{b}=-vec{c} times vec{b} `

`Rightarrow vec{a} times vec{b}+vec{c} times vec{b}=0 `

`Rightarrow(vec{a}+vec{c}) times vec{b}=0 text { ( Using right distributive property ) }`

Thus, `vec{a}+vec{c}` is parallel to` vec{b}. rightarrow vec{a}+vec{c}=m vec{b}`, for some scalarm .