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