Recent content by Yitin

Homework Statement Find parametric equations for the tangent line to the curve of intersection of the cone z=√(x2 + 4y2) and the plane 3z = x + 2y + 8 at the point (3,2,5) 2. The attempt at a solution I was trying to make the two Zs equal to each other, and solve for x or y, but I couldn't...

Thank you, that helped greatly, though I am still not the best at getting that curve. A later problem has z=√(x2 + 4y2) and 3z = x + 2y + 8 I was trying to make the two Zs equal to each other, and solve for x or y, but I couldn't get any of them separate. Same thing, finding the tangent...

Homework Statement I have to find the slope of the tangent line at (-1,1,5) to the curve of intersection of the surface z = x2 + 4y2 and the plane x = -1 2. The attempt at a solution I really am having trouble figuring out where to start. The question is even numbered, and the only one...

Ok, so now it should be (t5 +24t-5)2 (t10 + 48 + 576t-10) ||dr/dt|| = √( 1 + 3 + t10 + 48 + 576t-10 ) ||dr/dt|| = √( t10 + 52 + 576t-10 ) Which I am still not sure how to integrate, but it at least looks nicer.

Homework Statement Find arc length of the graph of r(t) = ti + ( (t6/6) - (6/t4) )j + t√3 k 1≤t≤2 Homework Equations Arc length = ∫ ||dr/dt|| dt (Integral from t0 to t1 of norm of derivative of r) The Attempt at a Solution dr/dt = i + (t5 + 24/(t3) )j + √3 k 12 = 1 (√3)2 = 3 (t5 + 24/(t3)...

I think I found the problem. When I set up the cross product, I accidentally put int a -8 instead of a 6. N should be <-148, 76, 20> And N ⋅ BC does = 0, as well as N ⋅ BD Thank you for your help Mark44.

Alright, so I did that and neither of them were 0. Now I have no idea where I went wrong.

Homework Statement B(-6,-7,-3) C(2,7,3) D(-4,-1,-11) Find the equations of the plane containing the triangle BCD. The attempt at a solution I've gotten to the end and got an equation, but the normal vector it has is just making me really paranoid. Vector BC = [2+6, 7+7, 3+3] =...