Video Transcript
What is the addition property that shows that vector 𝐚 plus negative vector 𝐚 is equal to the zero vector?
The property shown here is known as the additive inverse property. If we consider the integer 12, we know that adding negative 12 to this gives us zero. This same property holds when dealing with vectors. We recall that all elements of the zero vector are zero. For example, the two-dimensional zero vector is equal to zero, zero. If we let vector 𝐚 have components 𝑥 and 𝑦, then negative vector 𝐚 is equal to negative 𝑥, negative 𝑦. We know that when adding two vectors, we add their corresponding components. And since 𝑥 plus negative 𝑥 is equal to zero and 𝑦 plus negative 𝑦 is also equal to zero, we are left with a zero vector zero, zero. This confirms that vector 𝐚 plus negative vector 𝐚 is equal to the zero vector. And this is the additive inverse property.
