Question

Find the vector equation for the tangent line to the curve of intersection of x^2+y^2=25 and y^2+z^2=20 at (3,4,2)

Answer 1

Normal vector for x²+y²=25 is (2x,2y,0) = (6,8,0) ≡ (3,4,0) at given point
Normal vector for y²+z²=20 is (0,2y,2z) = (0,8,4) ≡ (0,2,1) at given point
Direction of tangent line = (3,4,0) X (0,2,1) = (4,−3,6)
Equation of line is r = (3,4,2) + t(4,−3,6)