Consider the intersection of the surfaces x² + y² = 1 and x + 2y + z = 0. (a) Sketch the surfaces and the curve of intersection. (b) Find a parametric equation r(t) = (x(t), y(t), z(t)) of the curve of intersection. Hint: Look at the projection of the curve onto the xy-plane, this is a circle which we already know how to parametrize. (c) Find the equation of the tangent line to the curve at the point (0, 1, -2). In other words, compute the tangent vector v of the curve at the point (0, 1, -2) and use the tangent vector to parametrize the line tangent to the curve at (0, 1, -2).

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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