Question

the rectangular box has a 2x2 base and height of 1. cosine of angle between AC and AB is...

Answer 1

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

Answer 2

We need to see the rest of the problem

Answer 3

i posted attachment

Answer 4

I know and it's not on that either

Answer 5

yes it is

Answer 6

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(?)

Answer 7

divide the problem into two right triangles

Answer 8

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.

Answer 9

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

Answer 10

or use dot product of AC with AB

Answer 11

The cosine of the angle is 2/3

Answer 12

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

Answer 13

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

Answer 14

the dot product of A and B is C

Answer 15

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

Answer 16

let me know if you need more help from here

Answer 17

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

Answer 18

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

Answer 19

no

Answer 20

o, sqrt(1+8)=3

Answer 21

so AC=3

Answer 22

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

Answer 23

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...

Answer 24

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

Answer 25

do you remember how to calculate the dot product part?

Answer 26

yes. mult component wise and then add

Answer 27

yep :)

Answer 28

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

Answer 29

exactly

Answer 30

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

Answer 31

no..the dot product only gives you cosines

Answer 32

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

Answer 33

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.

Answer 34

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

Answer 35

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

Answer 36

np

Answer 37

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

Answer 38

I get cos a = 2/3