## Calculus (3rd Edition)

$$u=-\sqrt 2 v=-\sqrt2(i-j).$$
The vector $u$ that has length $2$ and in the direction opposite to $v=i-j$ is given by $$u=-av=-a i +aj.$$ To find $a$, we have $$2=\sqrt{a^2+a^2}\Longrightarrow a=\sqrt 2$$ Hence, $$u=-\sqrt 2 v=-\sqrt2(i-j).$$