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A-level maths: Vectors Quiz

Authored by Hannah Ford

Mathematics

11th Grade

Used 8+ times

A-level maths: Vectors Quiz
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11 questions

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1.

FILL IN THE BLANK QUESTION

3 mins • 3 pts

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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?

2.

FILL IN THE BLANK QUESTION

5 mins • 5 pts

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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?

3.

FILL IN THE BLANK QUESTION

5 mins • 5 pts

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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?

4.

FILL IN THE BLANK QUESTION

10 mins • 6 pts

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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.

5.

OPEN ENDED QUESTION

10 mins • 6 pts

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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.

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6.

OPEN ENDED QUESTION

10 mins • 2 pts

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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.

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7.

FILL IN THE BLANK QUESTION

10 mins • 1 pt

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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

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