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.

• A
  Both $(i)$ and (ii) are true
• B
  Only $(i)$ is true,but (ii) is false
• C
  Only (ii) is true,but $(i)$ is false
• D
  Both $(i)$ and (ii) are false