Vector Algerbra and Geometry help

[AlphaThrone]

I don't understand what exactly K is in the red circle. How is it a constant if it's equal to 2n3/W and n1/H? Any help is appreciated.

 

[blamocur]

This looks completely out of context. What is being solved here? What is Q1.d?

 

[topsquark]

View attachment 33389
I don't understand what exactly K is in the red circle. How is it a constant if it's equal to 2n3/W and n1/H? Any help is appreciated.

It looks to me like H and W are also constants. The n's are merely the magnitudes of unit vectors, if I am reading the problem correctly.

It would help if you would show us Q1.d as well, for reference.

-Dan

 

[AlphaThrone]

This looks completely out of context. What is being solved here? What is Q1.d?

Sorry, Here is the full question, specifically ii).

 

[AlphaThrone]

It looks to me like H and W are also constants. The n's are merely the magnitudes of unit vectors, if I am reading the problem correctly.

It would help if you would show us Q1.d as well, for reference.

-Dan

Sorry, here is the full question. I get what H and W are, I just don't understand where the K comes in and what exactly it represents.

 

[blamocur]

I am assuming your question is about $k$, i.e., low-case, not $K$. If you have an equation with two variables of the type $An_1 = Bn_3$ then there are infinitely many solutions, but they all look like $n_1 = kB, n_3 = kA$, where $k$ is initially an arbitrary number. But since you are looking for a unit vector you need $n_1^2+n_3^2 = 1$, i.e. $k=\frac{1}{A^2+B^2}$.

 

[blamocur]

I am assuming your question is about $k$, i.e., low-case, not $K$. If you have an equation with two variables of the type $An_1 = Bn_3$ then there are infinitely many solutions, but they all look like $n_1 = kB, n_3 = kA$, where $k$ is initially an arbitrary number. But since you are looking for a unit vector you need $n_1^2+n_3^2 = 1$, i.e. $k=\frac{1}{A^2+B^2}$.

Ooops -- done it again : it's $k=\frac{1}{\sqrt{A^2+B^2}}$