Points relative to vectors. And Eq of line. Vectors

[Jbreezy]

Homework Statement

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.

Homework 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.

 

[Mark44]

Homework Statement

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.

Homework 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?

What are u, p, and q? All you said was that they are unit vectors that are orthogonal to each other.

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.

Didn't you post this as a separate question in your other thread?

 

[Jbreezy]

Mod note: Edited to properly show what was quoted.

What are u, p, and q? All you said was that they are unit vectors that are orthogonal to each other.

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>

 

[Mark44]

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

 

[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.

 

[Mark44]

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