Precalculus Vectors and Dot Product Quiz

What is the primary operation used to find the dot product of two vectors?

• Multiplication

• Division

• Subtraction

• Addition

How is the dot product of two vectors represented?

• As a vector

• As a matrix

• As a polynomial

• As a single number

What is the result of the dot product of two perpendicular vectors?

• Zero

• A negative number

• Undefined

• A positive number

How can the magnitude of a vector be found using the dot product?

• By multiplying the vector by a scalar

• By dividing the vector by its length

• By adding the components of the vector

• By taking the square root of the dot product of the vector with itself

What is the relationship between the dot product and the magnitude of a vector?

• The dot product is unrelated to the magnitude

• The dot product is the square of the magnitude

• The dot product is half the magnitude

• The dot product is twice the magnitude

What formula is used to find the angle between two vectors?

• Cross product

• Dot product divided by the product of magnitudes

• Cosine rule

• Sine rule

What is the cosine of the angle between two vectors equal to?

• The sum of the vectors

• The cross product of the vectors

• The difference of the vectors

• The dot product divided by the product of their magnitudes

How can you determine if two vectors are orthogonal?

• Their magnitudes are equal

• Their dot product is zero

• They have the same direction

• Their cross product is zero

What does it mean for two vectors to be parallel?

• They have the same direction or are scalar multiples of each other

• They intersect at a right angle

• Their dot product is zero

• They have the same magnitude

If two vectors have different slopes, what can be concluded about them?

• They are parallel

• They are identical

• They are neither orthogonal nor parallel

• They are orthogonal