Question

Which of the following is/are FALSE?

• A. $\overrightarrow{a}$ and $-\overrightarrow{a}$ are collinear
• B. Two collinear vectors are always equal in magnitude
• C. Zero vector is unique
• D. Two vectors having same magnitude are always collinear

Answer 1

Answer: (B), (D)

Two vectors having same magnitude are always collinear

Two or more collinear vectors will have same direction or opposite directions irrespective of their magnitudes. So $\overrightarrow{a}$ and $-\overrightarrow{a}$ are collinear vectors.

Two collinear vectors means two vectors are parallel, they may have different magnitude hence false.
Example: $\overrightarrow{a}$ and $2\overrightarrow{a}$
Both have same direction but different magnitude

Zero vector is always unique.

Two vector having equal magnitude cannot be always collinear.
Example: $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$, both have same magnitude$\left(\sqrt{2}\right)$ but different direction.