Vectors (Edexcel IGCSE Further Pure Maths): Exam Questions

The points and are the vertices of a quadrilateral such that

Show that is a parallelogram.

is extended to the point such that is a straight line.

Point lies on such that

Given that and are collinear,

find the vector in the form where and are rational numbers to be found.

Figure 2 shows triangle

where

(i) Find in terms of and

[2]

(ii) Find, in its simplest form, the exact value of

[1]

Figure 2 shows triangle

where

Find the area of triangle

Figure 2 shows triangle

where

The point lies on and such that , and are collinear.

Use a vector method to find vector as a simplified expression in terms of and

, and are fixed points such that

The unit vector parallel to is

Given that and re constants where and

find the exact value of

(i)

(ii)

Figure 3 shows quadrilateral where

The point is the midpoint of

Find as a simplified expression in terms of and

The point lies on such that , and are collinear.

Find the ratio

Figure 3 shows triangle with and

is the midpoint of .

is the point on such that

The lines and intersect at the point .

Find expressions, in terms of and , for

(i)

(ii)

Using a vector method, find