## anonymous 4 years ago the rectangular box has a 2x2 base and height of 1. cosine of angle between AC and AB is...

1. anonymous

2. anonymous

hints please, trying to solve on my own...

3. Mertsj

We need to see the rest of the problem

4. anonymous

i posted attachment

5. Mertsj

I know and it's not on that either

6. anonymous

yes it is

7. anonymous

you sure? i'm pretty sure it's solveable, just can't remember how...i believe the angle between the vector and AB (i'll label x axis) would be roh(?)

8. anonymous

divide the problem into two right triangles

9. anonymous

elica85. First, project the line down onto the base square of the triangle. Find the hypotenuse of the triangle that is formed by doing this. This is our adjacent quantity. We know the opposite quantity. Now we can use the tangent function.

10. anonymous

whoops. project the line down onto the base rectangle of the prism! sorry

11. anonymous

or use dot product of AC with AB

12. Mertsj

The cosine of the angle is 2/3

13. anonymous

ok, the dot product gives me the cosine? anything else i need to do after? and why dot produvct?

14. anonymous

because it gives you the cos of the angle, which is what you are trying to solve for

15. anonymous

|dw:1327112719359:dw|the dot product of A and B is C

16. anonymous

so,$A*B=|AC||AB|\cos \theta$

17. anonymous

let me know if you need more help from here

18. anonymous

Sorry I should have wrote $AC*AB=|AC||AB|\cos \theta$

19. anonymous

thx, still trying to understand...first how do i get AC...it would be sqrt(1^2+?^2)

20. anonymous

no

21. anonymous

o, sqrt(1+8)=3

22. anonymous

so AC=3

23. anonymous

AC=<2,2,1> so |AC|=(2^2+2^2+1^2)^1/2

24. anonymous

ok...i saw that dot product formula quite a few times but i don't get it. <AB>dot<AC>=|AB||AC|...and multiplied by cos...

25. anonymous

yeah, exactly. |AB||AC|cosa, where a i the angle between vectors AB and AC

26. anonymous

do you remember how to calculate the dot product part?

27. anonymous

yes. mult component wise and then add

28. anonymous

yep :)

29. anonymous

ok so have that on the left side...and then solve for cosa

30. anonymous

exactly

31. anonymous

ok ok. so use sina if the question asks to find the sine of the angle?

32. anonymous

no..the dot product only gives you cosines

33. anonymous

so if i'm asked for sine...?

34. anonymous

then you need to use another relation. if you have corresponding angles for example, you can relate the cos of one angle to the sin of another.

35. anonymous

ok, thx you closed the gap a lot for me just from this problem

36. anonymous

or the question might involve the cross-product of two vectors which involve the sin of the angle between the two vectors..depends on the problem

37. anonymous

np

38. anonymous

i get .84 but the closest out of the choices i have is 2/sqrt(5)...or none of the above

39. anonymous

I get cos a = 2/3