Question
Show that if $\mathbf{u}$ and $\mathbf{v}$ are orthogonal unit vectors, then $\mathbf{u} \times \mathbf{v}$ is also a unit vector.
Step 1
First, we know that the cross product of two vectors $\mathbf{u}$ and $\mathbf{v}$ is perpendicular to both $\mathbf{u}$ and $\mathbf{v}$. Show more…
Show all steps
Your feedback will help us improve your experience
Babita Kumari and 83 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that if $\mathbf{u}$ and $\mathbf{v}$ are orthogonal vectors, then $\|\mathbf{u} \times \mathbf{v}\|=\|\mathbf{u}\|\|\mathbf{v}\|$
Vectors; Lines, Planes, and Quadric Surfaces in Space
The Cross Product
Show that $\mathbf{u} \times \mathbf{v}$ is orthogonal to $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-\mathbf{v},$ where $\mathbf{u}$ and $\mathbf{v}$ are nonzero vectors.
Vectors in Space
Show that $\mathbf{v} \times \mathbf{u}$ is orthogonal to $(\mathbf{u} \cdot \mathbf{v})(\mathbf{u}+\mathbf{v})+\mathbf{u},$ where $\mathbf{u}$ and $\mathbf{v}$ are nonzero vectors.
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD