(c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t, 2t) and 1₂ (t) = (4 - 2t, 3 + 2t, 1 + 5t) are parallel. True False

18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² + 5x² is a maximum at P = (-1,2). (Use symbolic notation and fractions where needed. Give your answer in vector form.) direction: (b) Find the maximum value of the directional derivative. (Use symbolic notation and fractions where needed.) ||Vf(-1,2) || =

ri(t) = (-8, 10.5, – 5) + t (0, 3,0) r2(t) = (-12.5, 10.5, 1) + t (3, –1, –4) Find the point of intersection, P, of the lines rį and r2. P =

Find the orthogonal trajectories of the family of lines 3x + 5y = C A 3x - 5y = k 5x + 3y = k 3x + 5y = k 5x - 3y = k