题目
题目

SMAT011 Week 1 Practice Quiz

单项选择题

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 .

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思路分析
We are asked to find a vector orthogonal to both a = ⟨−2, −5, 1⟩ and b = ⟨1, 3, −2⟩. A standard way is to compute the cross product a × b, which yields a vector perpendicular to both a and b. Co......Login to view full explanation

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类似问题

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)

What is the area of the parallelogram spanned by the vectors (1,1,0) and (1,-1,0)?

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}

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