7. Given the vectors \( \mathbf{u}=6 \mathbf{i}+\mathbf{j}-3 \mathbf{k} \) and \( \mathbf{v}=2 \mathbf{i}+3 \mathbf{j}+\mathbf{k} \), then find a. the area of the parallelogram formed by \( \mathbf{u} \) and \( \mathbf{v} \). b. the area of the triangle formed by \( \mathbf{u} \) and \( \mathbf{v} \).
Added by Carlos G.
Close
Step 1
The area of the parallelogram formed by two vectors is given by the magnitude of their cross product. So, we first need to find the cross product of \( \mathbf{u} \) and \( \mathbf{v} \). The cross product of \( \mathbf{u} \) and \( \mathbf{v} \) is given by: \( Show moreโฆ
Show all steps
Your feedback will help us improve your experience
Guilherme Barros and 85 other Microeconomics 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
The vectors $\mathbf{P}$ and $\mathbf{Q}$ are two adjacent sides of a parallelogram. Determine the area of the parallelogram when $(a) \mathbf{P}=-8 \mathbf{i}+4 \mathbf{j}-4 \mathbf{k}$ and $\mathbf{Q}=3 \mathbf{i}+3 \mathbf{j}+6 \mathbf{k},(b) \mathbf{P}=7 \mathbf{i}-6 \mathbf{j}-3 \mathbf{k}$ and $\mathbf{Q}=-3 \mathbf{i}+6 \mathbf{j}-2 \mathbf{k}$
Rigid Bodies: Equivalent Systems of Forces
Forces and Moments
Find the area of the parallelogram determined by the given vectors $\mathbf{u}$ and $\mathbf{v}$. $$\mathbf{u}=(3,-1,4), \mathbf{v}=(6,-2,8)$$
Euclidean Vector Spaces
Cross Product
In Exercises 37-42, find the area of the parallelogram that has the vectors as adjacent sides. $\textbf{u} = -2\textbf{i}+3\textbf{j}+2\textbf{k}$ $\textbf{v} = \textbf{i}+2\textbf{j}+4\textbf{k}$
Analytic Geometry in Three Dimensions
The Cross Product of Two Vectors
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for APยฎ Courses
Economics
Watch the video solution with this free unlock.
EMAIL
PASSWORD