Vectors
GCE Further Mathematics

A position vector of point P is 3i + 4j and the position vector of point Q is 7i - 2j. (a) Find the vector PQ. (b) Find |PQ|, the magnitude of PQ. (c) Find the unit vector in the direction of PQ. (d) …

Two forces F1 and F2 act on a particle, where F1 = (5i + 2j) N and F2 = (-3i + 4j) N. (a) Find the resultant force R = F1 + F2. (b) Find the magnitude of R and the angle it makes with the positive x-a…

A vector has magnitude 10 and makes an angle of 60° with the positive x-axis. Find its y-component.

Given vectors m = 4i - 3j and n = -4i + 3j, which of the following statements is correct?

If the position vectors of points A and B are 3i + j and i + 5j respectively, find the unit vector in the direction of AB.

Given that a = 3i + 4j and b = i - 2j, find |a + b|.

The angle between vectors a = 2i + j and b = i + 2j is

Given that vectors p = (k+1)i + 3j and q = 2i + (k-2)j are perpendicular, find the value of k.

Points P, Q and R have position vectors p = i + 2j, q = 4i + 6j and r = 7i + 10j respectively. Which of the following correctly describes the relationship between P, Q and R?

Forces F₁ = (3i + 2j) N and F₂ = (i - 4j) N act on a particle. Find the magnitude of the resultant force.

If p = 2i + 3j and q = 5i - j, find p · q (the dot product of p and q).