Need help on vector analysis

by R3DH34RT
Tags: analysis, vector
 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 unit-normal 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...
 Sci Advisor HW Helper P: 2,482 What are the relevant equations? How do you define "normal"? What is a projection? How do you define "parallel"?
 P: 31 normal is perpendicular to the plane
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,348 Need help on vector analysis What do you know about the inner product of two perpendicular vectors?
 P: 31 The inner product of 2 perpendicular vector is zero, right? But, is there any relationship? :(
 P: 14 Do you have anymore information about D? What do you know about equations of a plane?
 P: 31 No, I don't have more information about D. I think that's already the equation of a plane? Thanks.
 Mentor P: 15,067 Let $\boldsymbol x_0 = (x_0, y_0, z_0)$ be some specific point on the plane. Let $\boldsymbol x = (x, y, z)$ be any point on the plane. Can you write equations that describe the points $\boldsymbol x_0$ and $\boldsymbol x$? What is the inner product of the vector from $\boldsymbol x_0$ to $\boldsymbol x$ with the vector $\boldsymbol n = (A,B,C)$?
 P: 31 D is just a constant. The equation of a plane is should be the normal of the vector, right?
 P: 31 Do you mean (x-x0)/x + (y-y0)/y + (z-z0)/z = 0? The inner product should be zero, right?
Mentor
P: 15,067
 Quote by R3DH34RT Do you mean (x-x0)/x + (y-y0)/y + (z-z0)/z = 0?
No. Where did you get the division?
 The inner product should be zero, right?
Yes, but this is what you need to prove.

Expanding on my previous post:
 Quote by D H Let $\boldsymbol x_0 = (x_0, y_0, z_0)$ be some specific point on the plane. Let $\boldsymbol x = (x, y, z)$ be any point on the plane.
Because both $\boldsymbol x_0$ and $\boldsymbol x$ are on the plane, $Ax_0 +By_0+Cz_0 = D$ and $Ax +By+Cz = D$.

(1) What is the difference between these equations?

(2) What is the vector from $\boldsymbol x_0$ to $\boldsymbol x$?

You are given that $\boldsymbol n = (A,B,C)$.

(3) What is the inner product between $\boldsymbol n$ and the vector from $\boldsymbol x_0$ to $\boldsymbol x$?

Don't guess. Use the answer to question 2. Finally, relate the answers to questions 1 and 3.
 P: 31 The vector from x0 to x is (x-x0) right? So should I do the inner product between (x-x0) . (n)? Then I won't get any number, just some equation in x n x0?
Mentor
P: 15,067
 Quote by R3DH34RT The vector from x0 to x is (x-x0) right? So should I do the inner product between (x-x0) . (n)?
Yes. Do that. The reason for doing this is that the vector $\boldsymbol x - \boldsymbol x_0$ represents any arbitrary vector on the plane. If a vector is normal to every vector on some plane the vector is normal to the plane itself.

 Then I won't get any number, just some equation in x n x0?
Please use English, not TXT-speak. Is it really that much harder to type x and x0?
 P: 31 OK... I'll do that... Can you please help me with number 2 and 3? Thanks :)
 P: 31 Hi, can anyone help me with the other question please...? I am so depressed... :( Need some hints... Thanks...
 Mentor P: 15,067 Redheart, you really do need to show some work before most people here will help you.
 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...
Math
Emeritus