Practice Mathematical Operations With Vectors (2) - A vector and its representation

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Calculate the dot product of vectors a = [1, 2, 3] and b = [4, 5, 6].
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Multiply corresponding components and add them.
Question 2.
What is the cross product of vectors a = [1, 0, 0] and b = [0, 1, 0]?
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Think of the right-hand rule for direction.
3Question 3.
What is the result of the dot product of two vectors?
- A vector
- A scalar
- A matrix
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Remember to consider the properties of scalar vs. vector.
4Question 4.
True or False: The cross product of two vectors is always orthogonal to the plane containing them.
- True
- False
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Think of how vectors interact in three-dimensional space.
Question 5.
Given vectors a = [3, 4] and b = [4, -3], calculate their dot product and interpret the result geometrically.
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Visualize the vectors on a graph.
Question 6.
Using a = [1, 2, 3] and b = [4, 5, 6], compute the tensor product and describe its significance.
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Focus on how each element in the result relates to each combination of inputs.

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