In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 3i + j, w = i + 3j

Video transcript

Hello, today we're going to be determining the dot product of A and B and the dot product of A and A. So we are given two vectors, we are given vector A as I plus 29 J and we are given vector B as 15, I plus J. Let's start by calculating the dot product of A and B. In order to calculate the dot product of A and B, we're going to take the product of the I components and J components together then take the sum of those two products. So the dot product of A and B will be defined as one multiplied by 15 plus 29 multiplied by one 15, multiplied by one will give us the value of 15 and 29 multiplied by one. Will give us the value of 29. Finally, 29 plus 15 will give us a final value of 44. And what this means is that the dot product of A and B is equal to 44. Next, let's calculate the dot product of A and A. Now, just like before, we'll need to take the product of the I and J components together. Then take the sum of those two products. But here we're multiplying vector A by itself. Let's go ahead and write out two instances of vector A. So if we take the dot product of A and A, we're going to be multiplying the coefficients of the I components and the coefficient of the J components, then take the sum of those components. So the dot product of A and A will be defined as one multiplied by one plus 29 multiplied by 29 one multiplied by one will give us the value of one and 29 multiplied by 29 will give us the value of 841. Finally, one plus 841 will give us the value of 842. And what this means is that the dot product of A and A is going to equal to 842. So just to summarize the dot product of A and B is the dot product of A and A is 842. With that being said, the answer to this problem is going to be B. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.