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Need help on vector analysis 
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#1
Sep2507, 02:20 PM

P: 31

Guys, I need ur help please... Can u help me to answer these problems? I'm very confused...
1. Show that the vector Ai + Bj + Ck is normal to the plane which equation is Ax + By + Cz = D, where A, B, C, D are constants 2. n = 0.5i + 0.5j + 0.7071k is the unitnormal for plane A. b = 4i + 5j + 2k, c = 2i + 3j + k. Calculate the area of parallelogram project from b x c to plane A. Calculate components of vectors b and c that are parallel to plane A. 3. New right hand coordinate axes are chosen at the same origin with e1' = (2e1 + 2e2 + e3)/3 and e2' = (e1  e2) x 1.4. Express e3' in term of e1. If t = 10e1 + 10e2  20e3, express t in terms of the new basis ek'. Express the old coordinate xi in term of xk' , xi = f(xk') Please help me guys... :( Thanks a lot... 


#2
Sep2507, 02:24 PM

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What are the relevant equations? How do you define "normal"? What is a projection? How do you define "parallel"?



#3
Sep2507, 02:31 PM

P: 31

normal is perpendicular to the plane



#4
Sep2507, 03:12 PM

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Need help on vector analysis
What do you know about the inner product of two perpendicular vectors?



#5
Sep2507, 07:38 PM

P: 31

The inner product of 2 perpendicular vector is zero, right?
But, is there any relationship? :( 


#6
Sep2607, 04:08 AM

P: 14

Do you have anymore information about D? What do you know about equations of a plane?



#7
Sep2607, 08:19 AM

P: 31

No, I don't have more information about D.
I think that's already the equation of a plane? Thanks. 


#8
Sep2607, 10:02 AM

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P: 15,147

Let [itex]\boldsymbol x_0 = (x_0, y_0, z_0)[/itex] be some specific point on the plane. Let [itex]\boldsymbol x = (x, y, z)[/itex] be any point on the plane. Can you write equations that describe the points [itex]\boldsymbol x_0[/itex] and [itex]\boldsymbol x[/itex]? What is the inner product of the vector from [itex]\boldsymbol x_0[/itex] to [itex]\boldsymbol x[/itex] with the vector [itex]\boldsymbol n = (A,B,C)[/itex]?



#9
Sep2707, 07:47 AM

P: 31

D is just a constant.
The equation of a plane is should be the normal of the vector, right? 


#10
Sep2707, 07:49 AM

P: 31

Do you mean (xx0)/x + (yy0)/y + (zz0)/z = 0?
The inner product should be zero, right? 


#11
Sep2707, 08:26 AM

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Expanding on my previous post: (1) What is the difference between these equations? (2) What is the vector from [itex]\boldsymbol x_0[/itex] to [itex]\boldsymbol x[/itex]? You are given that [itex]\boldsymbol n = (A,B,C) [/itex]. (3) What is the inner product between [itex]\boldsymbol n[/itex] and the vector from [itex]\boldsymbol x_0[/itex] to [itex]\boldsymbol x[/itex]? Don't guess. Use the answer to question 2. Finally, relate the answers to questions 1 and 3. 


#12
Sep2707, 08:40 AM

P: 31

The vector from x0 to x is (xx0) right?
So should I do the inner product between (xx0) . (n)? Then I won't get any number, just some equation in x n x0? 


#13
Sep2707, 08:51 AM

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#14
Sep2707, 10:52 PM

P: 31

OK... I'll do that...
Can you please help me with number 2 and 3? Thanks :) 


#15
Sep3007, 11:29 PM

P: 31

Hi, can anyone help me with the other question please...?
I am so depressed... :( Need some hints... Thanks... 


#16
Oct107, 02:52 AM

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P: 15,147

Redheart, you really do need to show some work before most people here will help you.



#17
Oct107, 11:58 AM

P: 31

I calculated the cross product of b x c, buat I don't know what is the meaning of "projection to plane A"
But for number 3, I can't figure out the meaning. Can you please give a hint? Thanks... 


#18
Oct107, 02:12 PM

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