The diagram shows two vectors 𝐀 and 𝐁. What is the scalar product of 𝐀 and 𝐁? Give your answer to two significant figures.
In this question, we’re presented with a diagram of two vectors and we’re asked to find the scalar product. We can see from the diagram that we have a vector 𝐀 with a magnitude of 3.2 and that we have a vector 𝐁 with a magnitude of 5.4. We also see that the angle 𝜃 between these two vectors is 130 degrees. Let’s recall that given two vectors 𝐀 and 𝐁, we can define their scalar product as equal to the magnitude of 𝐀 multiplied by the magnitude of 𝐁 multiplied by the cos of the angle 𝜃 between them.
Our diagram has provided us with values for all of the quantities on the right-hand side of this expression. We have the magnitude of 𝐀, we have the magnitude of 𝐁, and we have the value of 𝜃. So, let’s substitute in these values into this expression for the scalar product. Doing this, we get that the scalar product of 𝐀 and 𝐁 is given by 3.2, the magnitude of 𝐀, multiplied by 5.4, the magnitude of 𝐁, multiplied by the cos of 130 degrees, the angle 𝜃, between 𝐀 and 𝐁.
Evaluating this expression gives us the result 11.107 and so on with further decimal places. Looking back to the question, we see that we are told to give our answer to two significant figures. To this level of precision, our answer for the scalar product of the vectors 𝐀 and 𝐁 is 11.