Question

If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement: 
 \[\vec{a} = - \vec{b} \Rightarrow \left| \vec{a} \right| = \left| \vec{b} \right|\]

Answer 1

True.
\[\vec{a} = - \vec{b} \]
 Taking modulus on both sides of the equation, we get,
\[\left| \vec{a} \right| = \left| - \vec{b} \right|\]
\[\left| \vec{a} \right| = \left|  \vec{b} \right|\]                            [ ∵ \[\left| - \vec{b} \right| = \left| \vec{b} \right|\]]