[1 1 2] x [4 0 3] =nb: present result as the sum of the components. Ex.: [A B C]=A+B+C

Question

BlackTom AI · Accepted Answer

The question asks to evaluate the expression [1 1 2] x [4 0 3] and present the result as the sum of its components, i.e., compute the cross product and then sum the resulting vector's components.

First, recognize this as a cross product in 3D: a = [1, 1, 2] and b = [4, 0, 3]. The cross product a × b is a vector given by:
- x-component: a2*b3 − a3*b2 = 1*3 − 2*0 = 3
- y-component: a3*b1 − a1*b3 = 2*4 − 1*3 = 8 − 3 = 5 (note the negative sign in the standard formula makes this −(a3*b1 − a1*b3) = −(8 − 3) = 5, which matches directly when computed as shown below)
- z-component: a1*b2 − a2*b1 = 1*0 − 1*4 = 0 − 4 = −4

So the cross product vector is a × b = [3, 5, −4].

Now, present the result as the sum of its components: 3 + 5 + (−4) = 3 + 5 − 4 = 4.

Thus, the final value, expressed as the sum of the components of the cross product, is 4.

Dashboard ENG1062: Dynamics 1 (2024-25)

[1 1 2] x [4 0 3] =nb: present result as the sum of the components. Ex.: [A B C]=A+B+C

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[1 1 2] x [1 2 3] =nb: present result as the sum of the components. Ex.: [A B C]=A+B+C

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Dashboard ENG1062: Dynamics 1 (2024-25)

[1 1 2] x [4 0 3] =nb: present result as the sum of the components. Ex.: [A B C]=A+B+C

查看解析

登录即可查看完整答案

类似问题

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 .

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)?

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Let [math: u]{\bf u} and [math: v]{\bf v} be vectors in R3. What is the value of [math: u×v⋅v]{\bf u} \times {\bf v} \cdot {\bf v} ?

[1 1 2] x [1 2 3] =nb: present result as the sum of the components. Ex.: [A B C]=A+B+C

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希望你的学习变得更简单

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