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 are presented with a diagram of two vectors and asked to find their scalar product. We see from the diagram that we have a vector 𝐀 with a magnitude of 5.4 and that we have a vector 𝐁 with a magnitude of 6.7. The angle 𝜃 between these two vectors is 42 degrees. Let’s recall that we can define the scalar product of two vectors 𝐀 and 𝐁 as the magnitude of vector 𝐀 multiplied by the magnitude of vector 𝐁 multiplied by the cos of the angle 𝜃 between the two vectors. So let’s substitute in our values for the magnitude of 𝐀, magnitude of 𝐁, and the value of 𝜃 into this expression for the scalar product.
We have that the scalar product of 𝐀 and 𝐁 is equal to 5.4, the magnitude of 𝐀, multiplied by 6.7, the magnitude of 𝐁, multiplied by the cos of 42 degrees, the angle between our two vectors. If we evaluate this expression, we get the result 26.88697 and so on with further decimal places. Notice that the question asks us to give our answer to two significant figures. To this precision of two significant figures, our answer to the question of the scalar product of 𝐀 and 𝐁 is 27.