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Quiz

Year 3: Vectors in space

10 questions with solutions for year 3: dot, cross and triple products, angles between vectors, area and volume – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. x⃗ = p⃗ + q⃗, y⃗ = p⃗ − q⃗ and |p⃗| = |q⃗| = 3. What is the angle between x⃗ and y⃗ (degrees)?

2. a⃗ = 2p⃗ + q⃗, b⃗ = p⃗ − 2q⃗, |p⃗| = |q⃗| = 1, ∠(p⃗, q⃗) = π/3. The diagonals of the parallelogram are:

3. a⃗ = (2, −3, 1), b⃗ = (1, 2, −2). a⃗ × b⃗ = ?

4. Area of the parallelogram on a⃗ = (3, 1, 2) and b⃗ = (2, −2, 4):

5. Area of △ABC with AB⃗ = (−2, 3, −3) and AC⃗ = (1, 3, −5):

6. Area of the parallelogram with diagonals AC⃗ = (3, 1, −2) and BD⃗ = (1, −3, 4):

7. a⃗ = (1, 2x, −3) and b⃗ = (2, x, −2x) are perpendicular for x =

8. Is there an x for which a⃗ = (1, 2x, −3) and b⃗ = (2, x, −2x) are parallel?

9. Volume of the parallelepiped on a⃗ = (1, −1, 1), b⃗ = (2, 2, −1), c⃗ = (3, −1, 0):

10. Height of the parallelepiped on a⃗ = (3, −2, 5), b⃗ = (1, −1, 4), c⃗ = (1, −3, 1) with the base on a⃗ and b⃗: