Question

Answer the following as true or false.
(i) $\overrightarrow{a}$ and $-\overrightarrow{a}$ are collinear
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.

Answer 1

(i)

Two vectors are said to be be collinear vectors if they are parallel to the same line. In other words, any two parallel vectors are collinear.

Since, the negative of $\overrightarrow{a}$ i.e. $-\overrightarrow{a}$ is a vector having same magnitude but opposite direction.

So, $\overrightarrow{a},-\overrightarrow{a}$ are collinear vectors.

(iii)

Given statement is "False".
As collinear vectors are those vectors that are parallel to the same line.