Classify the following measure as a scalar or a vector:
$1000 \, cm^{3}$

If $a$ and $b$ are non-collinear vectors and $r$ is a vector coplanar with $a$ and $b$,then ......

Answer the following as true or false.
Two collinear vectors having the same magnitude are equal.

Which of the following is not a property of vectors?

Let $u$ and $v$ be non-collinear vectors in $\mathbb{R}^2$. Let $w$ be the orthogonal projection vector of $u$ on $v$. Consider two statements:
$(i)$ Any vector in $\mathbb{R}^2$ can be written as a linear combination of $u$ and $v$.
(ii) $w$ can be written as a linear combination of $u$ and $v$ as $w = au + bv$,where both $a$ and $b$ are non-zero real numbers.

The vectors $a = 2\hat{i} + 3\hat{j} + 6\hat{k}$ and $b$ are collinear and $|b| = 21$,then $b =$