## anonymous 3 years ago Vector Construction help! I've been stuck on this for some time, not sure what to do! Construct c = a + b by drawing and calculating the direction and magnitude of c. The direction should be measured from the +axis. // See illustration below.

1. anonymous

|dw:1381002960366:dw|

2. anonymous

to add 2 vectors you need to connect them tip to end

3. anonymous

Okay, I got that part but was confused where to go from there

4. anonymous

|dw:1381003142681:dw|

5. anonymous

Where do I go from there????

6. ganeshie8

drawing part of the question is over, next calculate mag and direction of a+b

7. anonymous

That's the part where I'm stuck!

8. anonymous

The mag would be found using pythagorean theorem right?

9. ganeshie8

to add vectors, u need to break them into components

10. anonymous

add the components bro

11. anonymous

?

12. anonymous

break vector into x component and y components then add x components and add y components

13. ganeshie8

|dw:1381003391274:dw|

14. ganeshie8

|dw:1381003459892:dw|

15. anonymous

Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?

16. anonymous

why pythagorean theorem

17. ganeshie8

first find the components of a+b

18. anonymous

for the magnitude

19. ganeshie8

x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

20. ganeshie8

ringt ?

21. ganeshie8

y components are in same direction, so u add them x components are in opposite directions, so u subtract them

22. anonymous

How do I know what to subtract from what?

23. ganeshie8

number line :)

24. ganeshie8

|dw:1381003731661:dw|

25. ganeshie8

|dw:1381003758234:dw|

26. ganeshie8

we follow that, if ur components are in that direction, they're +ve if they're in opposite, they're -ve

27. anonymous

Okay!

28. ganeshie8

x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

29. ganeshie8

once you have the x and y components for c, to get direction just use the samne formula, $$\theta = \large \tan^{-1} \frac{y}{x}$$

30. anonymous

31. ganeshie8

mag also same formula :- $$\large \sqrt{x^2+y^2}$$

32. ganeshie8

a+b is just a vector, so u can use same formulas

33. anonymous

That makes as a lot more sense, thank you so much!

34. anonymous

(again!)

35. ganeshie8

np :D

36. anonymous

@ganeshie8 I get 25 degrees for angle?

37. anonymous

@ganeshie8 ?

38. ganeshie8

looks wrong

39. ganeshie8

|dw:1381004400621:dw|

40. ganeshie8

check ur calculation again :)

41. ganeshie8

wolfram says below :- http://www.wolframalpha.com/input/?i=arctan%28%284.5sin%2860%29+%2B+8sin%2845%29%29%2F+%284.5cos%2860%29+-+8cos%2845%29%29%29 add 180 to it, to get into 2nd quadrant maybe

42. anonymous

ok

43. anonymous

@ganeshie8 What about if the vectors are being substracted then what do you do with the components for a and b? Is it the same like: we follow that, if ur components are in that direction, they're +ve if they're in opposite, they're -ve

44. anonymous

The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?

45. ganeshie8

yup !

46. ganeshie8

for mag just take sqrt(x^2+y^2)

47. ganeshie8