Question Video: Solving a Simple Vector Addition Mathematics • First Year of Secondary School

Video Transcript

If 𝐚 is the vector three, two and 𝐛 is the vector four, negative one, find 𝐚 plus 𝐛.

In this question, we’re given two vectors in two dimensions, the vector 𝐚 and the vector 𝐛. We need to find the sum of these two vectors; that’s the vector 𝐚 plus the vector 𝐛. And to do this, we recall that to add two vectors of the same dimension together, we just add the corresponding components together. Therefore, when we add these two vectors together, we’ll get another two-dimensional vector.

The first component of this vector is the sum of the first components of vector 𝐚 and vector 𝐛; that’s three plus four. And the second component of this vector will be the sum of the second components of vectors 𝐚 and 𝐛; that’s two plus negative one.

Now, all that’s left to do is evaluate the expression in each component. Three plus four is equal to seven, and two plus negative one is equal to one. This gives us the vector seven, one, which is our final answer.

Therefore, we were able to show if 𝐚 is the vector three, two and 𝐛 is the vector four, negative one, then 𝐚 plus 𝐛 is equal to the vector seven, one.