Suggested languages for you:

Americas

Europe

Problem 314

What is the angle between a diagonal of a cube and one of its edges?

Expert verified

The angle between a diagonal of a cube and one of its edges is 90°.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 14

Consider the vector space \(\mathrm{C}[0,1]\) of all continuous functions defined on \([0,1]\). If \(\mathrm{f} \in \mathrm{C}[0,1]\), show that $\left({ }^{1} \int_{0} \mathrm{f}^{2}(\mathrm{x}) \mathrm{d} \mathrm{x}\right)^{1 / 2}$ defines a norm on all elements of this vector space.

Chapter 14

Use the Gram-Schmidt process to transform \([(1,0,1),(1,2,-2),(2,-1,1)]\) into an orthogonal basis for \(\mathrm{R}^{3}\). Assume the standard inner product.

Chapter 14

Show that the functions $1, \cos \pi \mathrm{x}, \cos 2 \pi \mathrm{x}, \ldots, \cos \mathrm{n} \pi \mathrm{x}$, form an orthogonal set over \([0,1]\). Then normalize them to obtain an orthogonal set.

Chapter 14

Let \(\mathrm{X}=2 \mathrm{i}+\mathrm{j}+2 \mathrm{k}\) and $\mathrm{Y}=3 \mathrm{i}-\mathrm{j}-3 \mathrm{k}\(. Find \)\mathrm{X} \times \mathrm{Y}$.

Chapter 14

Find the area of the triangle determined by the points $\mathrm{P}_{1}(2,2,0), \mathrm{P}_{2}(-1,0,1)\( and \)\mathrm{P}_{3}(0,4,3)$ by using the cross-product.

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner