Find a unit vector orthogonal to both u and v. u = 8i - 16j + 4k v = 16i + 32j – 12k

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:**

Find a unit vector orthogonal to both **u** and **v**.

**Given Vectors:**

\[
\mathbf{u} = 8\mathbf{i} - 16\mathbf{j} + 4\mathbf{k}
\]

\[
\mathbf{v} = 16\mathbf{i} + 32\mathbf{j} - 12\mathbf{k}
\]

**Task:**

Calculate the cross product of **u** and **v** to find a vector orthogonal to both. Then, find the unit vector in the direction of this orthogonal vector.

**Note:**

There appears to be an empty text box with a red cross below the vectors, possibly indicating an incorrect or incomplete input.
Transcribed Image Text:**Problem Statement:** Find a unit vector orthogonal to both **u** and **v**. **Given Vectors:** \[ \mathbf{u} = 8\mathbf{i} - 16\mathbf{j} + 4\mathbf{k} \] \[ \mathbf{v} = 16\mathbf{i} + 32\mathbf{j} - 12\mathbf{k} \] **Task:** Calculate the cross product of **u** and **v** to find a vector orthogonal to both. Then, find the unit vector in the direction of this orthogonal vector. **Note:** There appears to be an empty text box with a red cross below the vectors, possibly indicating an incorrect or incomplete input.
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