Questions
MTH1030 -1035 - S1 2025 MTH1030/5 MTH1030/5 Week 1 lesson quiz: Vectors, lines and planes
Short answer
What is the area of the parallelogram spanned by the vectors (1,1,0) and (1,-1,0)?
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
We are asked to find the area of the parallelogram spanned by two vectors in R^3. The area of a parallelogram formed by vectors a and b is given by the magnitude of their cross product, |a × b|.
First, denote the vectors: a = (1, 1, 0) and b = (1,......Login to view full explanationLog in for full answers
We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!
Similar Questions
A vector that is orthogonal (perpendicular) to both vectors 𝑎 _ = ⟨ − 2 , − 5 , 1 ⟩ and 𝑏 _ = ⟨ 1 , 3 , − 2 ⟩ is: Hint: Vectors 𝑣 _ and 𝑤 _ are orthogonal if and only if 𝑣 _ ⋅ 𝑤 _ = 0 .
Let \(P\), \(Q\) and \(R\) be the points \[P = \left (-1, 2, -2\right ), Q = \left (-3, 3, -3\right ), R = \left (3, -3, 1\right ).\] Find a unit vector orthogonal to the plane through \(P\), \(Q\) and \(R\) that has a positive 1st component. What is its 3rd component?
Determine the result of the cross product of u=(1,0,0) and v=(0,1,0).(K:1)
Here are a couple of true statements. Make sure that you understand why all these statements are true. Once you do click "I get it :)". Cross your heart and ... :) The best way to make sense of these statements is to translate them into geometry. Okay, so let [math: u]{\bf u} and [math: v] {\bf v} be vectors in R3. The cross product only makes sense for vectors in R3.[math: u×v+v×u=0] {\bf u} \times {\bf v} +{\bf v} \times {\bf u} = {\bf 0}[math: (3u)×v=3(u×v)] (3 {\bf u}) \times {\bf v}= 3({\bf u} \times {\bf v} )If [math: u] {\bf u} is a multiple of [math: v] {\bf v} , then [math: u×v=0]{\bf u} \times {\bf v} = {\bf 0}[math: u×u=0] {\bf u} \times {\bf u} = {\bf 0}
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!