SET A4

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Calculus 3 Note: If you have already answered the problems in this post, kindly ignore it. If not, then answer it. Thank you, Tutor! Content Covered: - Cross Product and Scalar Product - Vector Projections and Direction Angles - Vector Operations (Dot Product) - Unit Vectors - Vectors in Plane and in Space Directions: Answer the problem below by showing the complete solution. In return, I will give you a good rating. Thank you so much! Note: Please be careful with the calculations in the problem. Kindly double check the solution and answer if there is a deficiency. And also, box the final answer. Thank you so much!

Find an equation of the tangent plane to the surface at the given point. z=B%Xy, til2,2) S (3) Find an equation of the tangent plane to the sun'ace at the given point. xyz = 15, {1, 3, 5} S {In} Find a set of symmetric equations for the normal line to the surface at the given point. OX+1=y+3=z5 15 3 5 OX+1=y+3=z5 15 5 3 OX1=y3=z5 15 5 3 Itm1=y3=z5 Oi== 15 3 5 Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = V x2 + 12, 9x - 3y + 42 = 35, (3, 4, 5)Find a unit normal vector to the surface at the given point. [Hint Normalize the gradient vector VFIZX, y, 2).] Surface Point In(y'_'z) = 0 (1, 9, 8) S