Suggested languages for you:

Americas

Europe

Q9E

Expert-verified
Found in: Page 564

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Find the resultant vector of $$({\rm{i}} \times {\rm{j}}) \times {\rm{k}}$$ using cross product.

The cross product $$({\rm{i}} \times {\rm{j}}) \times {\rm{k}}$$ is 0.

See the step by step solution

## Step 1: Formula used

Consider the following property

$$\begin{array}{l}{\rm{i}} \times {\rm{j}} = {\rm{k}}\\{\rm{k}} \times {\rm{k}} = 0\end{array}$$

## Step 2: Find the resultant vector

As given$$({\rm{i}} \times {\rm{j}}) \times {\rm{k}} \ldots \ldots \ldots (1)$$

According to formula,

$${\rm{i}} \times {\rm{j}} = {\rm{k}}$$

$${\rm{k}} \times {\rm{k}} = 0$$

Substitute $$k$$ for $$i \times j$$ in equation (1),

$$\begin{array}{l}({\rm{i}} \times {\rm{j}}) \times {\rm{k}} = {\rm{k}} \times {\rm{k}}\\({\rm{i}} \times {\rm{j}}) \times {\rm{k}} = 0\end{array}$$

Thus, the cross product $$({\rm{i}} \times {\rm{j}}) \times {\rm{k}}$$ is 0.