Section 10.8: Vectors

What is the magnitude of a vector v = 〈a, b〉?

• a^2 - b^2

• sqrt(a^2 + b^2)

• a + b

• a^2 + b^2

Which of the following represents a unit vector?

• A vector with magnitude 0

• A vector with magnitude 1

• A vector with magnitude greater than 1

• A vector with magnitude less than 1

How is a vector different from a line segment?

• A vector has neither magnitude nor direction

• A vector has only magnitude

• A vector has only direction

• A vector has both magnitude and direction

What is the result of scalar multiplication of a vector?

• Changes only the direction of the vector

• Changes only the magnitude of the vector

• Changes both magnitude and direction of the vector

• Has no effect on the vector

What is the dot product of two vectors v = 〈a, b〉 and u = 〈c, d〉?

• ac + bd

• a/c + b/d

• a + c + b + d

• a^2 + b^2 + c^2 + d^2

What is the component form of a vector with initial point (0,0) and terminal point (a,b)?

• (a, b)

• 〈a, b〉

• a + b

• a - b

What is the direction of a vector v = 〈a, b〉?

• tan^(-1)(b/a)

• cos^(-1)(a/b)

• tan^(-1)(a/b)

• sin^(-1)(b/a)

Which of the following is true for two equal vectors?

• They have the same magnitude but different directions

• They have different magnitudes and directions

• They have the same magnitude and direction

• They have different magnitudes but the same direction

What is the result of adding two vectors u and v?

• A complex number

• A matrix

• A new vector

• A scalar

What is the standard position of a vector?

• When its initial point is at (0,0)

• When it has no magnitude

• When it has no direction

• When its terminal point is at (0,0)