Video Transcript
Given that 𝐚 is the vector nine, one, find the vector 𝐚 plus the zero vector.
In this question, we’re given a vector 𝐚 and we’re asked to determine the vector 𝐚 added to the zero vector. And there’s two different ways we could answer this question. The easiest way to answer this question is to use the properties of vector operations. We can recall that the zero vector is called the additive identity of vector addition. This is because for any vector 𝐯 and zero vector of the same dimension as 𝐯, 𝐯 plus the zero vector is equal to vector 𝐯. Therefore, we can just apply this property to our question. The vector 𝐚 plus the zero vector is just equal to the vector 𝐚. And we know that 𝐚 is the vector nine, one, so this is equal to vector nine, one.
Let’s now also evaluate this vector expression directly to help show why this property holds true in general. We want to add the vector 𝐚 to the zero vector. 𝐚 is the vector nine, one. And since this is a two-dimensional vector, our zero vector will be the vector zero, zero. All of the components are equal to zero. Now, we recall to add two vectors of the same dimension together, we just add the corresponding components together. This gives us the vector nine plus zero, one plus zero. Since we’re adding the zero vector, we’re just adding zero to all of the components of 𝐚. But of course, adding zero to each component of this vector won’t change its value. So this is just equal to the vector nine, one.
