Question

The position vector for an electron is ${}^{\overrightarrow{\mathbf{r}}\mathbf{=}\left(5.0m\right)\hat{\mathbf{i}}\mathbf{-}\left(3.0m\right)\hat{\mathbf{j}}\mathbf{+}\left(2.0m\right)\hat{\mathbf{k}}}$.

(a) Find the magnitude of${}^{\mathit{r}}$. (b) Sketch the vector on a right-handed coordinate system.

Short answer

(a) The magnitude of vector ${}^r$is 6.2 m.

(b) The vector is drawn on a right handed coordinate system.

Step-by-step solution

Given data

The position vector for an electron,${}^{{}^{\overrightarrow{\mathrm{r}}=(5.0\mathrm{m})\hat{\mathrm{i}}-(3.0\mathrm{m})\hat{\mathrm{j}}+(2.0\mathrm{m})\hat{\mathrm{k}}}}$

Understanding the vector magnitude

A vector is a geometrical object with both magnitude and direction. The magnitude is the length of the vector.

The expression for the magnitude of a vector ${}^r$is given as:

… (i)

Here,${}^x$, y and z are the components of vectors in X, Y and Z-directions.

(a) Determination of the magnitude of vector r→

Using equation (i), the magnitude can be calculated as:

Thus, the magnitude of vector${}^r$ is${}^{6.2\mathrm{m}}$.

(b) To draw the vector diagram

The figure below shows the position vector for the electron.