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Questions and Answers
The norm of a vector is always a negative real number.
False
In Rn, the Euclidean distance of a vector x from the origin is given by x12 + · · · + xn2 .
True
The dot product of two nonzero vectors in Rn is kxkkyk cosθ.
False
The formula ku + vk2 = kuk2 + 2 Re(u, v) + kvk2 generalizes the law of sines in trigonometry.
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The Pythagorean Theorem is a generalization of the formula ku + vk2 = kuk2 + kvk2 when (u, v) = 0.
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The parallelogram law states ku + vk2 + ku − vk2 = 2kuk2 + 2kvk2 for all u and v in V.
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The parallelogram law is related to the law of tangents in trigonometry.
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Expanding norms squared of sums of vectors using bilinearity or sesquilinearity does not lead to any interesting formulas.
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The dot product of two nonzero vectors cannot be expressed using the cosine of an angle between them.
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The norm of a vector is always equivalent to the absolute value of the vector.
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