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Essential Calculus: Early Transcendentals
Found in: Page 564
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

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

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Short Answer

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 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.

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