Recent content by dcramps

Let me see if I understand your method... I am doing a dot product of QT and PR to get a vector T, the normal to the line, which I can use with a length formula to get what I need to know? What about the t parameter in PR?

Er, I forgot to mention that P = (2,3,1) Q = (3,5,3) R = (3,1,1) With that in mind, I don't think a dot product would work.

Homework Statement Find the distance from the point Q to the line passing through the points P and R. Homework Equations r=r0+tv D=|ax0 + by0 + cz0 + d| / sqrt(a2 + b2 + c2) The Attempt at a Solution To find the line: (x,y,z) = (2,3,1) + t(3-2,1-3,1-1) (x,y,z) = (2,3,1) + t(1,-2,0)...

Ah, right. That makes much sense. Thank you :) So you're just calculating [-x3- x5, -x3- 2x5, x3, 0, x5], then splitting it up into terms of x3 and x5, then factoring out?

Homework Statement Consider the matrix A: 1 4 5 0 9 3 -2 1 0 -1 -1 0 -1 0 -1 2 3 5 1 8 (Sorry I don't know how to do TeX matrices on this site) Find a basis for the row, column, and null space. Homework Equations The Attempt at a Solution I reduced to row echelon form, which...

Both answers were helpful. I do have another question though, since the solution given did not mention the origin. The solution to the question I asked above is: (x+x') + 2(y+y') + (z+z') = (x+2y+z) + (x'+2y'+z') = 6 + 6 = 12 thus (x+x') + 2(y+y') + (z+z') is not in P, and so P is not a...

This is a bit of a guess here, since I am a bit confused on the whole thing still, but I believe it must pass through the origin, and since it states x+2y+z=6, that is not satisfied...?

Homework Statement P={(x,y,z)|x+2y+z=6}, a plane in R3. P is not a subspace of R3. Why? Homework Equations See below. The Attempt at a Solution I am really quite confused here. My text says: "A subset W of a vector space V is called a subspace of V if W is itself a vector space...

Thanks for the tip and clarification :] I think you are correct, unless I made a mistake. Using this approach I found that all axioms were satisfied except axiom 5. Thoughts on this?

Homework Statement Homework Equations The 10 axioms: 1. If u and v are objects in V, then u + v is in V 2. u + v = v + u 3. u + (v+w) = (u+v)+w 4. There is an object 0 in V, called a zero factor for V, such that 0+u = u+0 = u for all u in V 5. For each u in V, there is an object -u in V...

Excellent. Thanks for your help :)

Thanks! Now I have my t and u values, and plugging them into the third equation gives me equality...but where do I go from here? Do I plug them into all of the original equations and use the results as my intersection point?

Homework Statement Find the point of intersection of two lines x = -9 + 5t y = 1 + t z = 10 - 4t and x = -2 -3t y = 5 + 2t z = 5 + 3t Homework Equations N/A The Attempt at a Solution I have read that you should set two of the equations equal to find the value of t, and...

I tried putting the system in the form you have, and I think you have made a mistake. The -3 in the last column should be a -1, no?

Thanks for the reply. I managed to get 2 and 3 on my own, but your advice on question 1 should be very useful. :)