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

Question

BlackTom AI · Accepted Answer

The problem presents two 3-element row vectors: [1 1 2] and [1 2 3], with a multiplication symbol that, given the result format, appears to denote a cross product in three dimensions.

Step 1: Interpret the operation. For two 3D vectors a = [a1, a2, a3] and b = [b1, b2, b3], the cross product a × b is the vector:
(a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1).
Applying this to a = [1, 1, 2] and b = [1, 2, 3]:
- First component: (1*3 - 2*2) = 3 - 4 = -1
- Second component: (2*1 - 1*3) = 2 - 3 = -1
- Third component: (1*2 - 1*1) = 2 - 1 = 1
Thus, a × b = [-1, -1, 1].

Step 2: Follow the instruction to present the result as the sum of the components. Sum the entries of the cross product vector:
(-1) + (-1) + 1 = -1.

Note on alternative interpretations: If one mistakenly treated the operation as a dot product, the result would be a single scalar equal to 1*1 + 1*2 + 2*3 = 1 + 2 + 6 = 9. If the operation were simple element-wise multiplication followed by summation, the vector would be [1, 2, 6] and the sum would also be 9. The given instruction and the resulting single-number value (-1) align with performing a cross product followed by summation of its components.

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

查看解析

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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 .

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