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

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- anonymous

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

- schrodinger

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- anonymous

##### 1 Attachment

- anonymous

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

- Mertsj

We need to see the rest of the problem

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- anonymous

i posted attachment

- Mertsj

I know and it's not on that either

- anonymous

yes it is

- 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(?)

- anonymous

divide the problem into two right triangles

- 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.

- anonymous

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

- anonymous

or use dot product of AC with AB

- Mertsj

The cosine of the angle is 2/3

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

let me know if you need more help from here

- anonymous

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

- anonymous

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

- anonymous

no

- anonymous

o, sqrt(1+8)=3

- anonymous

so AC=3

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

do you remember how to calculate the dot product part?

- anonymous

yes. mult component wise and then add

- anonymous

yep :)

- anonymous

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

- anonymous

exactly

- anonymous

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

- anonymous

no..the dot product only gives you cosines

- anonymous

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

- 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.

- anonymous

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

- 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

- anonymous

np

- anonymous

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

- anonymous

I get cos a = 2/3

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