Video Transcript
Vector 𝐀 is equal to three, four and vector 𝐁 is equal to five, three. Find the dot product of vector 𝐀 plus vector 𝐁 and vector 𝐀.
We will begin this question by adding vector 𝐀 and vector 𝐁. To add two or more vectors, we simply add their corresponding components. In this case, we need to add three and five and then four and three. The vector 𝐀 plus 𝐁 is therefore equal to eight, seven. We need to find the dot product of this vector and vector 𝐀. We know that if two vectors 𝐮 and 𝐯 have components 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two, respectively, then their dot product is a scalar quantity. It is equal to 𝑥 one multiplied by 𝑥 two plus 𝑦 one multiplied by 𝑦 two.
In this question, we need to find the dot product of vectors eight, seven and three, four. This will be equal to eight multiplied by three plus seven multiplied by four. Eight multiplied by three is 24, and seven multiplied by four is 28. This gives us a total of 52.
If vector 𝐀 is equal to three, four and vector 𝐁 is equal to five, three, then the dot product of vector 𝐀 plus 𝐁 and vector 𝐀 is 52.
