Displacement Vectors and Parallelograms

This tutorial covers position and displacement vectors, explaining the difference between them and how to calculate displacement vectors. An example is provided to demonstrate the calculation of a displacement vector between two points. The tutorial also includes a problem involving a parallelogram, where the position vector of a point is determined using vector properties. The solution is verified, and the tutorial concludes with a summary of the concepts covered.

What is the primary focus of this tutorial?

• Studying quadratic equations

• Understanding scalar multiplication

• Exploring position and displacement vectors

• Learning about matrix transformations

How do you calculate the displacement vector between two points?

• Add the position vectors of both points

• Subtract the position vector of the first point from the second

• Multiply the position vectors of both points

• Divide the position vector of the second point by the first

What is the displacement vector from point A (3, 2) to point B (8, 12)?

• (11, 14)

• (5, 10)

• (8, 12)

• (3, 2)

Why is it important to verify the displacement vector calculation?

• To determine if the vector is parallel

• To check if the vector is perpendicular

• To confirm the calculation is correct

• To ensure the vector is a unit vector

What is a key property of a parallelogram?

• All sides are equal

• Diagonals are perpendicular

• Opposite sides are parallel and equal

• All angles are right angles

In a parallelogram, if one pair of opposite sides is parallel, what can be said about the other pair?

• They are perpendicular

• They are also parallel

• They are equal in length

• They are not parallel

How can the properties of a parallelogram help in finding missing coordinates?

• By calculating the area of the parallelogram

• By using the Pythagorean theorem

• By ensuring opposite sides are equal and parallel

• By using trigonometric identities

What is the position vector of point D if it forms a parallelogram with points A, B, and C?

• (-2, 7)

• (-3, 0)

• (4, 9)

• (3, 2)

If BC is the same as AD in a parallelogram, what does this imply?

• BC is twice the length of AD

• BC and AD are equal in length and direction

• BC and AD are not related

• BC is perpendicular to AD

What is the result of adding the displacement vector (-6, -2) to the position vector (3, 2)?

• (-3, 0)

• (-6, -2)

• (0, 0)

• (3, 2)