Proving Collinearity of Points Using Vector Methods

The video tutorial explains a vector problem involving a triangle OAB, where C is the midpoint of OA, D is on AB with a ratio of 3:1, and E is such that OB equals twice BE. The task is to prove that points C, D, and E are collinear using vector methods. The tutorial guides through diagram creation, vector calculations, and proof of collinearity, emphasizing careful processing of information and correct representation in diagrams.

What is the initial setup of the triangle OAB in terms of vectors?

• O to A is vector a, and O to B is vector b.

• O to A is vector b, and O to B is vector a.

• O to A is vector a, and O to B is vector c.

• O to A is vector c, and O to B is vector b.

Where is point C located in relation to OA?

• At the endpoint of OA

• At the endpoint of OB

• At the midpoint of OA

• At the midpoint of OB

What is the ratio of AD to DB?

• 1:3

• 3:1

• 2:1

• 1:2

How is point E positioned relative to OB?

• O to B is equal to B to E

• O to B is half B to E

• O to B is twice B to E

• O to B is three times B to E

What is the vector expression for A to B?

• A - B

• B - A

• B + A

• A + B

How do you calculate the vector from C to D?

• 1/2 A + 3/4 B

• 1/4 A + 3/4 B

• 3/4 B - 1/4 A

• 1/4 B - 3/4 A

What is the vector expression for C to E?

• 3/2 B - 1/2 A

• 1/2 B - 3/2 A

• 3/4 B - 1/4 A

• 1/2 A + 3/2 B

What common factor is used to factorize the vectors for C to D and C to E?

• 1/4

• 3/2

• 3/4

• 1/2

What is the relationship between the lengths of CD and CE?

• CD is twice CE

• CE is twice CD

• CD is equal to CE

• CD is half of CE

What was the first mark awarded for in the marking scheme?

• Accurate representation of information using a diagram

• Correct calculation of C to E

• Proving that D is a common point

• Correct calculation of C to D