What is a vector?
A directed segment defined by its origin, direction, sense, and magnitude.
What makes a basis orthonormal?
Its basis vectors are mutually perpendicular and each has magnitude 1.
What does the dot product of basis vectors and equal when ?
1.
What is the dimension of the Euclidean space considered?
Three dimensions.
How are two vectors in added componentwise?
Their corresponding components are added.
What components result from adding vectors and ?
What form defines a linear combination of vectors through ?
, with each real.
What does linear independence require when a combination of vectors equals zero?
Every coefficient must be zero.
What is the dot product of two vectors in terms of magnitudes and angle?
The product of their magnitudes and the cosine of the angle between them.
How is the dot product calculated from three components in an orthonormal basis?
Answer 11 questions on Vector Algebra and Calculus.
1. Which set of attributes defines a vector represented by a directed segment?
2. A vector is known to have a direction, sense, and magnitude, but neither its supporting line nor its point of application is specified. How is it classified?
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