# Points relative to vectors. And Eq of line. Vectors

1. May 8, 2013

### Jbreezy

1. The problem statement, all variables and given/known data
Find the coordinates of α, β, and γ rel. to u, p, q (unit vectors) of x = 1/9( 2i + 62j - 11k )(
(Note there orthogonal to each other)

Question 2 : The position vectors of two points A, B has position vectors a = < 2, 1, 7> and
b = <1, 4,-1>
Find the parametric vector eq of the line AB using lambda as parameter.
2. Relevant equations

For the first question I just did the dot product of x with each unit vector.
I ended up with σ = 2 , β = 3 , γ = 6
What do you think?

For the next question please don't give me an answer give me a question to direct my though if it is incorrect. Thanks.

So I said x = a + λb
Where b is a unit vector. Is this proper? I didn't want to expand it and write the vectors it will look a mess.
I have the unit vector b = < 1/ (3sqrt 3), 4/ (3 sqrt 3), -1/ (3sqrt 3)>
I think this is proper.

2. May 8, 2013

### Staff: Mentor

What are u, p, and q? All you said was that they are unit vectors that are orthogonal to each other.
Didn't you post this as a separate question in your other thread?

3. May 9, 2013

### Jbreezy

Mod note: Edited to properly show what was quoted.
What do you mean what are they? I don't understand.
Yeah I posted this first then I thought not to clump so just ignore the second question. Thanks.

Sorry they are

q = < 4/9 , 7/9 , -4/9 >
u = < 1/9, 4/9 , 8/9 >
p = < -8/9, 4/9 , -1/ 9>

Last edited by a moderator: May 9, 2013
4. May 9, 2013

### Staff: Mentor

The problem is to write x = <2/9, 62/9, -11/9> as a linear combination of u, p, and q.

In other words, you want to find constants a, b, and c (didn't see the point in using Greek letters) so that
x = au + bp + cq

5. May 9, 2013

### Jbreezy

Yeah and I got σ = 2 , β = 3 , γ = 6, so x = 2u + 3p + 6q
assuming that I kept that in the right order. and your a = alpha , b = beta, c = gamma.
I just had greek because the problem used it.

6. May 9, 2013

### Staff: Mentor

This letter -- σ -- is sigma (lower case). This one is alpha - α.