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

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

A small sculpture made of brass is believed to have a secret central cavity. The weight of the sculpture in air is 15.76 N. When it is submerged in water, the weight is 13.86 N. What is the volume of the secret cavity?

Find the domain and range and describe the level curves for the function f(x,y).f(x, y) =

Solve the problem.A force of magnitude 14 pounds pulling on a suitcase makes an angle of 60° with the ground. Express the force in terms of its i and j components.

Match the equation with the surface it defines.x2 + y2 = 1