- #1

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Find the components of

__d__=(3,5,7) along the directions of

__u__,

__v__and

__w__

consider:

__u__=1/3(2,2,-1)

__v__=1/3(2,-1,2)

__w__=1/3(-1,2,2)

I don't know where to start, I need some ideas to solve this

thanx

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- Thread starter harshakantha
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- #1

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Find the components of

consider:

I don't know where to start, I need some ideas to solve this

thanx

- #2

ehild

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Start with the definition of "component of a vector". Think of scalar product.

ehild

ehild

- #3

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- #4

ehild

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ehild

- #5

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I don't understand, with which do I need to multiply?? can you show me how to do that?

- #6

ehild

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ehild

- #7

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How do I suppose to calculate **du**? by using the scalar product??

- #8

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after solving **du**=x1**uu**+x2**vu**+x3**wu**, I got 27 for x_{1} is this correct ehild?

- #9

ehild

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No, how did you get it?

ehild

ehild

- #10

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(3,5,7)1/3(2,-2,-1)=x

- #11

ehild

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What did you get for the individual products **du**, **uu**, **vu**, **wu**?

ehild

ehild

- #12

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- #13

ehild

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Yes, but how much is uu?

ehild

ehild

- #14

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oops I've made a mistake when solving , is **UU**=1, then I got 3 for x_{1}

- #15

ehild

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Note: this method works for orthogonal u, v ,w vectors only. In general, you can write a linear system of equations for x1,x2,x3 and solve it.

ehild

- #16

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- #17

ehild

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You can make an unit vector of any vector by dividing all components by the modulus.

Can I help something more?

ehild

- #18

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Note: this method works for orthogonal u, v ,w vectors only. In general, you can write a linear system of equations for x1,x2,x3 and solve it.

ehild

I found 3, 5 and 7 respectively for the components x

I had to Find the components of d=(3,5,7) along the directions of u, v and w

consider: u=1/3(2,2,-1) v=1/3(2,-1,2) w=1/3(-1,2,2), finally I got 3,5,7. this is really confusing me

- #19

ehild

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3u, 5v and 7 w, that is: d=3u+5v+7w. Check.

ehild

- #20

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3u, 5v and 7 w, that is: d=3u+5v+7w. Check.

ehild

Thanx ehild, then what is my final answer would be?

- #21

ehild

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It depends how "component" was defined during your classes; I would say 3u, 5v, 7w.

ehild

ehild

- #22

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Thanx a lot ehild bye..

- #23

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You can make an unit vector of any vector by dividing all components by the modulus.

Can I help something more?

ehild

thanks ehild your post really helpful to me, now I got a more clear idea about mutually perpendicular unit vectors :), bye..

- #24

ehild

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Splendid!

ehild

ehild

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