(Solved): roblem 1. [18 points] The following two questions are independent of one another. a) Consider the c ...

roblem 1. [18 points] The following two questions are independent of one another. a) Consider the curve \( C \) with parametrization \( r(t)=(\cos t, \sin t, \sin t) \). Write the parametric equations for the tangent line to this curve at the point \( P=\left(\frac{\sqrt{3}}{2}, \frac{1}{2}, \frac{1}{2}\right) \) b) Let \[ f(x, y, z)=x^{2}+y^{2}+z^{2} \] At the point \( (1,2,1) \), find the rate of change of \( f \) in the direction perpendicular to the plane \( 2 x+4 y+3 z=3 \). pointing away from the origin.