Calculus 3 :

Section 10.5: Problem 21 (1 point) Results for this submission Entered Answer Preview Result Message 0 correct 1 correct O correct incorrect incorrect Variable 'o' is not defined in this context incorrect incorrect correct -3 -3 incorrect At least one of the answers above is NOT correct. Consider the planes 31 + ly + 2z = 1 and 32 + 2z = 0. (A) Find the unique point P on the y-axis which is on both planes. ( 0 . 1 0 (B) Find a unit vector u with positive first coordinate that is parallel to both planes. 1 2 i+ oj + 3 k (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes. r(t) = 2 i + 1 j+ -3 k Note: You can earn partial credit on this problem. Preview My Answers Submit AnswersSection 10.7: Problem 1 (1 point) Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -oo and use "INF" for oo as necessary, and use "U" for a union symbol if a union of intervals is needed. a) r(t) = (In(20t), v+ + 3, b) r(t) = (vt -5, sin (Of), (2) c) r(t) = (estSection 10.7: Problem 10 (1 point) Find parametric equations for the tangent line at the point (cos (: "), sin (* *), =*) on the curve r = cost, y = sint, = = t I(t) = y(t)= =(t)= (Your line should be parametrizationsses through the given point at (=0).Section 10.7: Problem 4 (1 point) The curve c(t) = (cost, sint, t) lies on which of the following surfaces. Enter T or F depending on whether the statement is true or false. (You must enter T or F -- True and False will not work.) 1. a sphere 2. a circular cylinder 3. an ellipsoid 4. a planeSection 10.7: Problem 5 (1 point) Match the parametric equations with the graphs labeled A- F. As always, you may click on the thumbnail image to produce a larger image in a new window (sometimes exactly on top of the old one). 1. I = cos 4t, y = t, z = sin 4t 2. I = cost, y = sint, z = Int 3. I = sin 3t cost, y = sin 3t sint, > = t 4. x = cost, y = sint, z = sin 5t 5. 1 =t, y = 1/(1+(3), 2=12 6. x = t' - 2,y =1,z=f*+ 1 A B C D E FSection 10.7: Problem 6 (1 point) Find a vector function that represents the curve of intersection of the paraboloid & = 328 + 4y and the cylinder y = 212. Use the variable t for the parameter. r(t) = (t].Section 10.7: Problem 7 (1 point) Consider the paraboloid z = 12 + y?. The plane 4x - 5y + z - 9 = 0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrization of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2"pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface. c(t) = (I(t), y(t), z(t)), where I(t) = y(t) z(t)=Section 10.7: Problem 8 (1 point) Find the derivative of the vector function r(t) = In(12 -+ )i + v7 + ti - Be "k r'(t) =(0 0. 0>Section 10.7: Problem 9 (1 point) For the given position vectors r(#) compute the unit tangent vector T(#) for the given value of t . A) Let r(t) = (cos 5t, sin 5t). Then T(# )( B) Let r(t) = (#],13). Then T(3) =(].> CLetr(t) = elite "jfth Then T(-2)= k