Question

What is obtained when every vector is added to its opposite vector, satisfying \[\vec{a} + (-\vec{a})\]?

Options

• Twice the vector \[2\vec{a}\]

• A unit vector \[\hat{a}\]

• The original vector \[\vec{a}\]

• The zero vector \[\vec{0}\]

Answer 1

Every vector has an additive inverse (an opposite vector \(-\vec{a}\)). When a vector is added to its additive inverse, the result is the zero vector: \[\vec{a} + (-\vec{a}) = \vec{0}\].