Video Transcript
Fill in the blank: If vector 𝐀 and vector 𝐁 are two perpendicular vectors, then vector 𝐀 dot vector 𝐁 equals what.
Let’s begin this question by modeling these two perpendicular vectors, vector 𝐀 and 𝐁. Because we’re told that these two vectors are perpendicular, then that means that we know that the angle between them is 90 degrees. And so what exactly is the vector 𝐀 dot vector 𝐁? Well, that’s the dot product. The dot product of two vectors tells us what amount of one vector goes in the direction of another. The dot product of two vectors 𝐀 and 𝐁 is defined as the magnitude of vector 𝐀 times the magnitude of vector 𝐁 times the cos of 𝜃, where 𝜃 is the angle formed between vector 𝐀 and vector 𝐁.
In the case of these two perpendiculars, vector 𝐀 and vector 𝐁, we know that the angle between the vectors is 90 degrees. Although we don’t know the magnitude of vector 𝐀 and vector 𝐁, we can say something about the cos of 90 degrees. We should remember that the cos of 90 degrees is zero. And so we can say that the dot product of vector 𝐀 and 𝐁 is zero. And so that will be the missing value in this statement. In fact, this is a general definition that we should learn and use. Two vectors 𝐀 and 𝐁 are perpendicular if and only if their dot product is equal to zero, that is, vector 𝐀 dot vector 𝐁 is equal to zero. And so the missing value in this statement is that vector 𝐀 dot vector 𝐁 is equal to zero.
