## Statement

difficulty

Find the position vector and its magnitude for the following points:

a) P1 (-1,2)
b) P2 (-3,4)

## Solution

Question a)

Applying the definition of position vector:

$\stackrel{\to }{r}=x\stackrel{\to }{i}+y\stackrel{\to }{j}+z\stackrel{\to }{k}$

Since our body is located at point (- 1,2) then x=-1, y=2 and z=0. Substituting x, y and z in the definition of position vector for this point we get:

Once we have the position vector, to calculate its magnitude we just apply the equation:

$\left|\stackrel{\to }{r}\right|=\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$

and substituting the corresponding values:

Question b)

Applying the same equations that in the previous question, we get that for point P2 (-3,4), the position vector (r2) is:

and its modulus:

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$\left|\stackrel{\to }{r}\right|=\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$
$\stackrel{\to }{r}=x\stackrel{\to }{i}+y\stackrel{\to }{j}+z\stackrel{\to }{k}$