Answer
$$u=-\sqrt 2 v=-\sqrt2(i-j).$$
Work Step by Step
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,
$$u=-\sqrt 2 v=-\sqrt2(i-j).$$
