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Q9E

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Essential Calculus: Early Transcendentals

Found in: Page 564

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

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

Most popular questions for Math Textbooks

To find a dot product \(u \cdot v\) and \(u \cdot w\).

(a) To determine

To find: A nonzero vector orthogonal to the plane through the points \({\bf{P}}\), \({\bf{Q}}\) and \(R\).

(b) To determine

To find: The area of triangle \({\bf{PQ}}R\).

Show the equation \(0 \times {\rm{a}} = 0 = {\rm{a}} \times 0\) for any vector \({\rm{a}}\) in \({V_3}\).

(a) Find all vectors \({\bf{v}}\) such that

\(\langle 1,2,1\rangle \times {\bf{v}} = \langle 3,1, - 5\rangle \)

(b) Explain why there is no vector \({\bf{v}}\) such that

\(\langle 1,2,1\rangle \times {\bf{v}} = \langle 3,1,5\rangle \)

To find a dot product between \({\rm{a}}\) and \({\rm{b}}\).

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