Q) Suppose that the following two vectors u and v are perpendicular. Write the number b in terms of a.
$$u=\begin{pmatrix}2 \\-2 \\\end{pmatrix}$$
and $$v=\begin{pmatrix}a \\b \\\end{pmatrix}$$
What I did is that, since u and v are perpendicular, their product should be equal to zero. So,
$u \cdot v=0$
$2a+(-2b)=0$
$2a-2b=0$
$b=a$
Is this right? I'm not sure because this question carries 6 marks, and even the steps are not 6.
The answer is correct. You used the assumption that the vectors are perpendicular, so dot product is zero. Then you solved for $a$ in terms of $b$. So $a$ is a fixed point of $b$.