IB Math SL



IB Math SL Name_____________________________________________

HW 1 – Intro to 3D Vectors

1. Find the magnitude of each of these vectors.

a. 4i + 3j b. 5i – 7j c. 2i – 2j + k

d. 6i – 3j + 4k e. [pic] f. [pic]

g. [pic] h. [pic]

2. Given v = xi + 5j - [pic]k and [pic] = 9, find the possible values of the constant x.

3. Given that [pic] = 6, find the possible values of the constant y.

4. Find the possible values of the constant a such that [pic] = 13.

5. Find a unit vector in the direction of the vector 8i – 6j.

6. Find a unit vector in the direction of v = 5i – 8j.

7. Find a unit vector in the direction of the vector [pic]

8. Find a unit vector in the direction of v = 3i – 2j + 5k.

9. Find a unit vector in the direction of the vector i - 3j + 2k.

10. Find a unit vector in the direction of the vector [pic]

11. Find a vector of magnitude 14 in the direction of the vector 6i – 3j + 2k.

12. Find a vector of magnitude [pic]in the direction of v = 4i – 8k.

13. Find a vector of magnitude [pic]in the direction of the vector [pic]

14. Given that [pic]= 2i – 4j + 5k and [pic] = 3i + 6j – 2k, find [pic]

15. Given that [pic] = -2i +3j – 6k and [pic] = 5i – 7k, find [pic]

16. Given that [pic]= 5i – 7j – 2k and [pic]= 2i – 3j – 2k, find [pic]

17. Given that [pic]= 10i – 4j – 6k and [pic]= 7j – 5k, find [pic]

18. Given that [pic] = [pic]and [pic]= [pic] find [pic]

19. Given [pic]= xi + 6j + 4k, [pic] = 4i + yj – 3k and [pic] = -3i + zk, find the values of the constants x, y, and z.

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