Necesito ayuda con el ejercicio #31?

<img src="https://tex.z-dn.net/?f=%5Ctextbf%7BSoluci%5C%27on%20al%20ejercicio%2031%7D.%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BEl%20vector%20ortogonal%20al%20plano%20%7D%5CPi_1%5Ctexttt%7B%20es%20%7D%5Cvec%20%7Bp_1%7D%3D%283%2C-4%2C%5Clambda%29%5Ctexttt%7B%20y%20el%20vector%7D%5C%5C%0A%5Ctexttt%7Bortogonal%20al%20plano%20%7D%5CPi_2%5Ctexttt%7B%20es%20%7D%5Cvec%7Bp_2%7D%3D%282%2C-3%2C6%29%5C%5C%20%5C%5C%0A%5Ctexttt%7BSe%20desea%20que%20%7D%5Cvec%7Bp_1%7D%5Cbot%5Cvec%7Bp_2%7D%5Ctexttt%7B%20es%20decir%20%7D%5Cvec%7Bp_1%7D%5Ccdot%5Cvec%7Bp_2%7D%3D0%5Cto%283%2C-4%2C%5Clambda%29%5Ccdot%282%2C-3%2C6%29%3D0%5C%5C%20%5C%5C%0A6%2B12%2B6%5Clambda%3D0%5Cto%20%5Cboxed%7B%5Clambda%20%3D%20-3%7D" />.