Exam 10: Vectors and the Geometry of Space

A bicycle pedal is pushed by a foot with a force of a-N as shown. The shaft of the pedal is cm long.Find the magnitude of the torque about P correct to two decimal places.Let N, , .

Find the distance between the point and the plane Round your answer to two decimal place.

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Find an equation of the sphere with center that touches the xy-plane.

Find the standard equation of the sphere with center C and radius r.C (3, -5, 3); r = 7

Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

Find the center and the radius of the sphere that has the given equation. + + - 6x + 4y = 0

Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is times the distance from P to the yz-plane.

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

The position function of a particle is given by When is the speed a minimum?

Find the acceleration of a particle with the given position function.

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.A (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line

Find the distance from to the xy-planes.

Find the scalar tangential and normal components of acceleration of a particle with position vector

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Find the length of the curve

Classify the surface.

Find the velocity of a particle that has the given acceleration and the given initial velocity.

Reduce the equation to one of the standard forms.