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After messing around a bit, I found that a) xy = (x+\dfrac{y}{4})^2 - (x-\dfrac{y}{4})^2 Signature: (1,-1) b) Similar to a): yz = (y+\dfrac{z}{4})^2 - (y-\dfrac{z}{4})^2 Signature: (1,-1,0) c) Continuing from before, and using b); (x+y+z)^2 - yz = (x+y+z)^2 + (y-\frac{z}{4})^2 -...

Homework Statement Complete the square to determine the signature of the following quadratic forms: a) h(x,y) = xy b) h(x,y,z) = yz c) h(x,y,z) = x^2 + y^2 + z^2 + 2xy + 2xz + yz Homework Equations The Attempt at a Solution I suspect there's a really simple trick to this...

Wow, I should reply to these things more quickly. Thank you for looking over my work. Also, thank you for providing me with that shortcut. Realizing that sooner would have made things a lot easier, but hopefully I learned something along the way...

I ran through the arithmetic of my solution again, and realized that I forgot to divide one of the coordinates of one of the points on Pm by two. So, in step (5), I've chosen (2/3, 1/3, 5/3) on Lv and (2/5, 1, 1/5) on Lu, both being a distance of 1 away from the the intersection point Ps of the...

Homework Statement A light ray with direction (1, 2, -2) passes through the point (-1, -3, 5) and is reflected farther away on a plane. The reflected ray has the direction (3, 0, 4) and passes through the point (4, 1, 5). Determine the equation for the plane which reflects the ray. The...

Awesome! That works out! Thanks again for your assistance! :D By the way, I think it should be a plus sign rather than a minus sign in front of (2/3)m, but that's trivial. Okay, so finally: \left\{ \begin{array}{ccc} 1-m- \frac{n}{2} & = & 0 \\ \frac{2}{3} m - \frac{n}{2} & = & 0 \end{array}...

No, that looks good. Thanks for your help, by the way. :) Okay, so, since \mathbf{a}=\vec{AB} and \mathbf{b}=\vec{AC}, we get... \vec{QC} = \vec{AC} - \vec{AQ} = \mathbf{b} - (2/3) \mathbf{a} ...and... \vec{AR} = ... = \vec{AC} - m \vec{QC} = \mathbf{b} - m(\mathbf{b} - (2/3) \mathbf{a}) =...

I'm not sure if I understood you entirely, but I assigned \overrightarrow{AR} = n \cdot \overrightarrow{AP} \overrightarrow{RP} = (1-n) \cdot \overrightarrow{AP} \overrightarrow{RC} = m \cdot \overrightarrow{QC} \overrightarrow{QR} = (1-m) \cdot \overrightarrow{AP}. So, we've got...

That's the thing. I'm unable to find any of the interior vectors QR, AR, PR or CR in terms of any of the other vectors. If I could do that, the problem would be trivial. I don't think that brute force is applicable, since no relation is given between sides AB and BC (not that I haven't tried)...

Homework Statement In triangle ABC, the point P bisects the side BC, the point Q is the point on side AB for which |AQ| = 2|QB|, and the point R is the point of intersection between AP and CQ. Designate vectors a=AB and b=AC. Describe vector AR in terms of vectors a and b. Homework...