The vectors $\begin{pmatrix} \cos\theta \\ -\sin\theta \end{pmatrix}$ and $\begin{pmatrix} \sin\theta \\ \cos\theta \end{pmatrix}$ are a. orthogonal b. both unit vectors (length 1) c. both of the above
Added by Catherine B.
Close
Step 1
Step 1: The dot product of two vectors is given by the formula: a · b = |a| |b| cos(θ), where θ is the angle between the two vectors. Show more…
Show all steps
Your feedback will help us improve your experience
Jerry Zhang and 94 other Calculus 3 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
$1-2=$ Let $\mathbf{u}=\left\langle a_{1}, a_{2}\right\rangle$ and $\mathbf{v}=\left\langle b_{1}, b_{2}\right\rangle$ be nonzero vectors in the plane, and let $\theta$ be the angle between them. The angle $\theta$ satisfies $$\cos \theta=$$ So if $\mathbf{u} \cdot \mathbf{v}=0,$ the vectors are _______________.
Vectors in Two and Three Dimensions
The Dot Product
Two vectors $\mathbf{A}$ and $\mathbf{B}$ are inclined to each other at an angle $\theta$. Which of the following is the unit vector perpendicular to both $\mathbf{A}$ and $\mathbf{B}$ ? (a) $\frac{\mathrm{A} \times \mathrm{B}}{\mathrm{AB}}$ (b) $\frac{\hat{\mathrm{A}} \times \hat{\mathrm{B}}}{\sin \theta}$ (c) $\frac{A \times B}{A B \sin \theta}$ (d) $\frac{A \times B}{A B \cos \theta}$
Vector Analysis
Round 2
The magnitude of vector A ,B,C are 12,5,13 unit respectively, and vector A+B =C ,The angle between vector A and B
Adi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD