Chapter 11, Problem 49RE

To determine

To find: The cross product of given two vector.

Answer to Problem 49RE

$4i+2j-4k$

Explanation of Solution

Given information:

Two vectors are given as,

$\begin{array}{l}\text{u}=2i+3j+2k\\ \text{v}=3i+j+2k\end{array}$

Concepts used:

Cross product of two vectors $\text{u}=\langle x_1,y_1,z_1\rangle \text{ and v}=\langle x_2,y_2,z_2\rangle$ is given as −

$\text{u}\times \text{v}=\left|\begin{array}{ccc}i& j& k\\ x_1& y_1& z_1\\ x_2& y_2& z_2\end{array}\right|$

Calculation:

Giventwo vectors are −

$\begin{array}{l}\text{u}=2i+3j+2k\\ \text{v}=3i+j+2k\end{array}$

So, cross product of these two vector will be given as-

$\begin{array}{l}\text{u}\times \text{v}=\left|\begin{array}{ccc}i& j& k\\ 2& 3& 2\\ 3& 1& 2\end{array}\right|\\ \Rightarrow \text{u}\times \text{v}=i\left[3\times 2-1\times 2\right]-j\left[2\times 2-3\times 2\right]+k\left[2\times 1-3\times 3\right]\\ \Rightarrow \text{u}\times \text{v}=i\left(6-2\right)-j\left(4-6\right)+k\left(2-6\right)\\ \Rightarrow \text{u}\times \text{v}=4i+2j-4k\end{array}$

Hence, cross product of given two vectors is $4i+2j-4k$ .