Video Transcript
If the scalar projection of vector 𝐀 along vector 𝐁 is 𝐴 sub 𝐵 equals one and the dot or scalar product of vectors 𝐀 and 𝐁 is equal to two, find the magnitude of vector 𝐁.
We begin by recalling that the scalar projection of vector 𝐀 onto vector 𝐁 is equal to the magnitude of vector 𝐀 multiplied by cos 𝜃. This can be demonstrated in a diagram as shown. An alternative form for the equation of the projection of vector 𝐀 onto vector 𝐁 is the dot product of vectors 𝐀 and 𝐁 divided by the magnitude of vector 𝐁.
In this question, we are told that the dot product of vectors 𝐀 and 𝐁 is equal to two. And we need to calculate the magnitude of vector 𝐁. We are also told that the scalar projection of vector 𝐀 along vector 𝐁 is equal to one. Substituting the given values into the second equation, we have one is equal to two divided by the magnitude of vector 𝐁. Multiplying through by the magnitude of vector 𝐁, we have the magnitude of vector 𝐁 equals two. This is the final answer to this question.
