Unit Vector and Dot Product Practice - Annapolis High School



Unit Vector and Dot Product Practice

Unit 2.2 Vectors

IB HL 2

Answer the following:

1. Given coordinates A = (7, -3) and B = (-2, 5), write vector AB in the form of xi + yj.

2. If A = (-2, 8, 4) and B = (-7, -5, -11), write vector BA in the form of xi + yj + zk.

3. Let a = 4i – j + 5k, b = 3i + 7j – 2k and c = -2i + 2j + 3k. Find 2a – 4b + 3c. Write the answer in the form of a column vector.

4. The vectors a = 3j + 8k and B = xi +5k are of equal length. Find x.

5. Find the lengths of the following vectors, expressing your answers as surds. It is not necessary to simplify these surds.

a. 5i – 3j

b. -2i + 7j

c. 4i – 3j + 2k

6. Find the magnitude of a = [pic].

7. Find the unit vector in the direction of 6i – 4j + 3k.

8. Find the vector of length 16 in the direction of [pic].

9. Find the scalar products of these pairs of vectors:

a. 3i + 2j and 2i + 3j

b. 6i + j – k and –7i – 4j + 3k

c. –i + 5j + 4k and 5i – 4k

10. Find the scalar product of a = 5i + 2j – k and b = 3i – 4j + 4k and the angle between a and b in radians.

11. Let u = 3i + 2j – 5k and v = i – 7j + 4k. Find u • v and the angle between u and v in radians.

12. Let u = 4i + 7j – 2k and w = 8i – Pj + 2k. Find the value of P so that u and w are perpendicular.

13. Find the angle between the vectors 7i + 8j and –4i + 9j.

14. Two vectors are defined as a = 2i + xj and b = i – 4j. Find the value of x if the vectors are perpendicular.

15. Two vectors are defined as a = 2i + xj and b = i – 4j. Find the value of x if the vectors are parallel.

16. Find the value(s) for x for which the vectors xi + j – k and xi – 2xj – k are perpendicular.

17. P, Q and R are three point in space with the coordinates (2, -1, 4), (3, 1, 2) and (-1, 2, 5) respectively. Find angle Q in the triangle PQR.

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