10 Questions
What is the defining characteristic of a scalar quantity?
It can be expressed by its magnitude and units alone
What property of vector addition states that the order of the addends does not affect the sum?
Commutative property
Which of the following is a defining characteristic of a unit vector?
Its magnitude is one
What property of scalar multiplication states that the product of a vector and the sum of two scalars is equal to the sum of the products of the vector with each scalar?
Distributive property
The dot product of two vectors is defined as $|u||v|\cos\theta$. What does the angle $\theta$ represent?
The angle between the two vectors
Which property states that the scalar product of vectors is commutative?
a. The scalar product of vectors is commutative: u ⋅ v = v ⋅ u
Which property states that the scalar product is distributive over vector addition?
c. Distributivity: u × (v + w) = u × v + u × w
What is the result of the cross product of a vector with itself?
d. u × u = 0
Which property states that the cross product of two vectors is orthogonal to both vectors?
a. (u × v) ⋅ u = (u × v) ⋅ v = 0
What is the result of the triple scalar product u ⋅ (v × w)?
d. u ⋅ (v × w) = (u × v) ⋅ w
Test your knowledge on vector quantities with this quiz covering concepts such as scalar quantities, vector quantities, equality of vectors, zero vectors, and unit vectors.
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