Question

Sa se descompuna vectorul v= -5i+j dupa directiile vectorilor a= i+j si b= -i+2j. Va roog

Answer 1

Salut.

$\vec{v}=m\cdot\vec{a}+n\cdot\vec{b},\ va\ trebui\ s\breve{a}\ afl\breve{a}m\valorile\ m,\ n\in\mathbb{R}.\\\\-5\vec{i}+\vec{j}=m(\vec{i}+\vec{j})+n(-\vec{i}+2\vec{j}),\ sau\ -5\vec{i}+\vec{j}=m\vec{i}+m\vec{j}-n\vec{i}+2n\vec{j},\ sau\\\\-5\vec{i}+\vec{j}=(m-n)\vec{i}+(m+2n)\vec{j}.$

De aici:

--5 = m -- n => m = n -- 5

1 = m + 2n, deci 1 = n -- 5 + 2n, adică 3n = 6, deci n = 2, iar m = --3. La final:

$\vec{v}=-3\vec{a}+2\vec{b}$

Green eyes.