Exam 11: Vectors and the Geometry of Space

Find the vector v with the given magnitude and the same direction as

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is

Find the vector v with the magnitude and direction of

Find the magnitude of the vector v given its initial and terminal points.Round your answer to four decimal places. Initial point: (-2, -4, -5) Terminal point: (-3, -9, -10)

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent. U: (6,5), (9,11) v: (3,-5), (6,1)

Given sketch the graph of

Given

Suppose the guy wire to a 100-foot tower has a tension of 500 pounds.Using the distances shown in the figure, write the component form of the vector F representing the tension in The wire.Round numerical values in your answer to the nearest integer.

The vector v and its initial point is given.Find the terminal point. , initial point

Find the unit vector in the direction of u.

Find the standard equation of the sphere with center (2, 8, 4), and radius 2.

Suppose a plane flies at a constant groundspeed of 500 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest.Both the airspeed and the compass direction Must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to Maintain its groundspeed and eastward direction.Round your answer to two decimal places.

Given

Find the component form of the vector u with the given initial and terminal points. Initial point: (5, 7, 8 ) Terminal point: (-2 , 10 , 10 )

Suppose a plane flies at a constant groundspeed of 600 miles per hour due east and encounters a 10 mile-per-hour wind from the northwest.Both the airspeed and the compass direction Must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to Maintain its groundspeed and eastward direction.Round your answer to two decimal places.

Find the vector

Given the vector v lies in the yz-plane, has magnitude 8, and makes an angle of with the positive y-axis.Find the component form of v.

Find the standard equation of the sphere with center at and tangent to the yz-plane.

Find the magnitude of the vector given below.Round your answer to four decimal places.

Find the distance between the points given below. (-4, 2, -3 ), ( 0, 5, 1 )