For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the given parameter value r(t) = (7t2 – 7t)i + (t + 3)j + k ; t0 = 2

Find the vector projv u v = 3i – j + 3k, u = 2i + 10j + 11k

Calculate the arc length of the indicated portion of the curve r(t).r(t) = 11t3i + 2t3j + 10t3k, -1 ≤ t ≤ 2

Find the vector projv u v = 3i – j + 3k, u = 2i + 10j + 11k

Solve the problem.Find the area of the triangle determined by the points P(-3, 6, -4), Q(9, -6, 7), and

The position vector of a particle is r(t). Find the requested vector.The acceleration at t = 0 for r(t) = t2i + (4t3 – 9)j + k

Solve the problem.Find the area of the triangle determined by the points P(-3, 6, -4), Q(9, -6, 7), and

Give a geometric description of the set of points whose coordinates satisfy the given conditions.x2 + y2 + z2 = 36, z = 5

Find the principal unit normal vector N for the curve r(t).r(t) =(6t cos t – 6 sin t)j + (6t sin t + 6 cos t)k

For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the given parameter value r(t) = (7t2 – 7t)i + (t + 3)j + k ; t0 = 2