4.8 Vectors

Define a vector in the context of a directed line segment.

Explain how you would plot a vector P_1P_2 with two components in the xy-plane. What do the terms a and b represent in this context?

Describe the direction and magnitude of a vector when it is represented geometrically in the plane.

How would you find the components of a vector represented geometrically in the plane using trigonometry?

What is the result of the multiplication of a constant and a vector? How does it affect the original vector?

Explain how the sum of two vectors in R^2 is found and how it can be represented graphically.

What is the dot product of two vectors? How is it calculated?

Define a unit vector. How can you find a unit vector in the same direction as a given nonzero vector?

Given vector V = (2, 3), find a unit vector in the same direction.

If A = (4, 2) and B = (1, 3), calculate A + B.

Vector V has an angle of 45 degrees with the x-axis and a magnitude of 5. Find the components of V.

If A = (2, 3) and B = (4, -1), find the dot product of A and B.

Determine whether vectors A = (1, 2) and B = (-2, -4) are parallel.

Given that A = (3, 2), find a vector B such that the dot product of A and B is zero.

Express vector V = (2, 3) in the form ai + bj.

Find the magnitude of vector A = (-4, 3).

If a vector V makes an angle of 60 degrees with the positive x-axis and its x-component is 4, find the y-component of V.

Given vectors A = (2, 3) and B = (4, -1), find 3A - 2B.

Two vectors A = (a_1, b_1) and B = (a_2, b_2) are given. Prove that if their dot product is zero, then the vectors are perpendicular.

Given vectors A = (1, 2) and B = (3, 4), find a vector C such that A + B + C = 0.

Given a vector V = (2, 3), find a scalar k such that the magnitude of kV is 10.

Given two vectors A = (2, 3) and B = (4, -1), if B is the resultant of A and another vector C, find the vector C.

Find the angle between vectors A = (1, 2) and B = (2, 2). Use the dot product and the concept of magnitude in your solution.