Question Video: Finding the Norm of Vectors Mathematics

Video Transcript

If the vector 𝐀 is equal to two, negative five, two, find the magnitude of 𝐀.

Remember, this notation is asking us to find the magnitude of 𝐀. That’s the distance between an initial point and the end point at 𝐀. This is a position vector. So we’re looking to find the distance between 𝐀 and the origin. And there’s a formula we can use. It’s an extension of the Pythagorean theorem. And it says that the magnitude of a vector 𝑣 given by 𝑥𝑖 plus 𝑦𝑗 plus 𝑧𝑘 or 𝑥, 𝑦, 𝑧 is given by the square root of 𝑥 squared plus 𝑦 squared plus 𝑧 squared.

Let’s substitute what we know about our vector 𝐀 into the formula. 𝑥 is two. 𝑦 is negative five. And 𝑧 is also two. So the magnitude of 𝐀 is the square root of two squared plus negative five squared plus two squared. Two squared is four. And negative five squared is 25. So the magnitude of 𝐀 is found by the square root of four plus 25 plus four, which is 33.

So the magnitude of 𝐀 is root 33.