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Vector Quantities Quiz

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Questions and Answers

What is the defining characteristic of a scalar quantity?

It can be expressed by its magnitude and units alone (correct)

It can be expressed by its magnitude, direction, and units

It can be expressed by its magnitude and direction

It can be expressed by its direction and units alone

What property of vector addition states that the order of the addends does not affect the sum?

Identity property

Multiplicative property

Commutative property (correct)

Associative property

Which of the following is a defining characteristic of a unit vector?

Its direction is indeterminate

Its direction is opposite to the original vector

Its magnitude is one (correct)

Its magnitude is zero

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 Signup and view all the answers

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 Signup and view all the answers

Which property states that the scalar product of vectors is commutative?

a. The scalar product of vectors is commutative: u ⋅ v = v ⋅ u Signup and view all the answers

Which property states that the scalar product is distributive over vector addition?

c. Distributivity: u × (v + w) = u × v + u × w Signup and view all the answers

What is the result of the cross product of a vector with itself?

d. u × u = 0 Signup and view all the answers

Which property states that the cross product of two vectors is orthogonal to both vectors?

a. (u × v) ⋅ u = (u × v) ⋅ v = 0 Signup and view all the answers

What is the result of the triple scalar product u ⋅ (v × w)?

d. u ⋅ (v × w) = (u × v) ⋅ w Signup and view all the answers