Consider two vectors:

a=(1,0,1)and b=(1,0,-1)

Are these vectors orthogonal?

Question

Consider two  vectors:

a=(1,0,1)and b=(1,0,-1)

Are these vectors orthogonal?

BlackTom AI · Accepted Answer

Let's analyze the question by recalling what it means for two vectors to be orthogonal.

Given vectors a = (1, 0, 1) and b = (1, 0, -1), compute their dot product: a · b = (1)(1) + (0)(0) + (1)(-1) = 1 + 0 - 1 = 0.

A dot product of zero indicates that the vectors are perpendicular to each other in the Euclidean space, which is the standard definition of orthogonality for vectors in R^3.

Note about the provided data: the question appears to be a multiple-choice prompt, but the list of answer options is missing here. In a typical setup, you would select the option that states the vectors are orthogonal since the dot product is zero.

To verify the reasoning, you can always revisit the definition: two vectors are orthogonal if their dot product equals zero; this is independent of the magnitudes of the vectors. If either vector were scaled or rotated while maintaining a nonzero dot product, they would not be orthogonal, illustrating why the zero result is the key criterion.

Consider two vectors: a=(1,0,1)and b=(1,0,-1) Are these vectors orthogonal? 单项选择题

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