Question

Which statement is/are true ?

• A. Two non-zero non-collinear vectors are linearly dependent.
• B. Any two collinear vectors are linearly independent.
• C. Two non-zero non-collinear vectors are always linearly independent.
• D. $A$ and $B$ both are true.

Answer 1

Answer: (A), (C)

The correct options are
A Two non-zero non-collinear vectors are linearly dependent.
C Two non-zero non-collinear vectors are always linearly independent.

let two no zero vectors

$\overrightarrow{a},\overrightarrow{b}$

both are collinear

$\overrightarrow{a}=\lambda \overrightarrow{b}$

from here It is clear that vectors are linear dependent

and if vectors are non collinear

the vectors can be linear dependent but are always linearly independent