A-level maths: Vectors Quiz

The points A, B, C and D have coordinates (2, 1, 3), (4, 1, 5), (2, 5, p) and (q, r, 1) respectively. If AB = CD what are the values of p, q and r?

Points A and B have coordinates (2, 1, 1) and (20, -5, 13) respectively. If point C is such that 2AC = CB, what are the coordinates of C?

The point P has coordinates (-2, 4, 0). The point Q is such that PQ = [3, -2, -1]. The point R has coordinates (1, 1, r). For which value of r is PQR an equilateral triangle?

Point A has coordinates (2, 3, 6). Point B has coordinates (8, 6, 8). Find the point C so that AB and AC are in the same direction and |AC| = 77.

Forces F₁ = λ(2i - 3j + k)N and F₂ = μ(i + j + 3k)N, where λ and μ are scalars, act on a box. Prove that it is not possible for their resultant force to act in the direction of k.

The points P, Q and R have position vectors [3, -1, 4], [2, -3, 0] and [7, 1, 3] respectively.

(a) Show that the triangle PQR is isosceles.

The points P, Q and R have position vectors [3, -1, 4], [2, -3, 0] and [7, 1, 3] respectively.

(b) M is the midpoint of QR. Find the position vector of M, giving your answer in the form ai +bj +ck

The points P, Q and R have position vectors [3, -1, 4], [2, -3, 0] and [7, 1, 3] respectively.

(c) Calculate the area of the triangle PQR giving your answer to 3 sf (units not required)

The points A, B, C and D have position vectors [2, -1, 4], [-3, -1, 14], [-11, 4, 20] and [-6, 4, 10] respectively.

(a) write down the vector AB

The points A, B, C and D have position vectors [2, -1, 4], [-3, -1, 14], [-11, 4, 20] and [-6, 4, 10] respectively.

(b) calculate the length BC giving your answer to 3sf