Question

What is the magnitude of vector `AB` if `A= (4,2,-6)` and `B=(9,-1,3)`?

Answer 1

Let `\vec A` be the position vector of A and `\vec B` be the position vector of B. A position vector is a vector that points from the origin to a particular point.

If you plot `\vec A`, `\vec B` and `\vec {AB}`, then you can easily notice that `\vec B = \vec A + \vec{AB}` using the triangle rule of addition of vectors. (Try it for two-dimensional vectors!)

In this question, `\vec A = 4\hat i + 2\hat j - 6 \hat k` and `\vec B = 9\hat i - \hat j + 3 \hat k`. So `9\hat i - \hat j + 3 \hat k = (4 \hat i + 2 \hat j - 6 \hat k )+ \vec {AB}`, thus meaning that `\vec {AB} = (9 - 4) \hat i + (-1 - 2) \hat j + (3 + 6)\hat k = 5\hat i - 3\hat j + 9 \hat k`.