Adding and Subtracting Rational Expressions Explained

What defines a vector in mathematical terms?

• A quantity with magnitude only

• A quantity with neither magnitude nor direction

• A quantity with direction only

• A quantity with both magnitude and direction

How is the magnitude of a vector typically represented?

• Through its color

• Through its label

• Through its position

• Through its length

What is the standard position of a vector?

• Originating at any point

• Originating at the origin

• Originating at the endpoint

• Originating at the midpoint

How do you calculate the magnitude of a vector?

• Sum of its components

• Square root of the sum of the squares of its components

• Product of its components

• x-component plus y-component

What trigonometric function is used to find the direction angle of a vector?

• Tangent

• Cotangent

• Sine

• Cosine

What is the result of adding two vectors?

• A vector with combined magnitude

• A vector with combined components

• A vector with the smallest magnitude

• A vector in the opposite direction

How can you verify two vectors are equivalent?

• By their color

• By their labels

• By their positions

• By comparing their component forms

What does multiplying a vector by a negative scalar do?

• Changes its components

• Changes its magnitude

• Does not change it

• Changes its direction

What is the effect of subtracting one vector from another?

• Results in a vector pointing in the same direction

• Results in a vector with increased magnitude

• Results in a vector pointing in the opposite direction

• Results in a vector with decreased magnitude

How do you find the horizontal component of a vector in standard position?

• Magnitude divided by the cosine of the angle

• Magnitude divided by the sine of the angle

• Magnitude times the cosine of the angle

• Magnitude times the sine of the angle