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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