Problem 61E: Consider a rectangular box with one of the vertices at the origin, as shown in the following figure.... Problem 62E: Find the coordinates of point P and determine its distance to the origin. Problem 63E: For the following exercises, describe and graph the set of points that satisfles the given equation.... Problem 64E: For the following exercises, describe and graph the set of points that satisfles the given equation.... Problem 65E: For the following exercises, describe and graph the set of points that satisfles the given equation.... Problem 66E: For the following exercises, describe and graph the set of points that satisfles the given equation.... Problem 67E: Write the equation of the plane passing through point (1,1,1) that is parallel to the xy -plane. Problem 68E: Write the equation of the plane passing through point (1,3,2) that is parallel to the xz -plane. Problem 69E: Find an equation of the plane passing through points (1,3,2),(0,3,2) and (1,0,2) . Problem 70E: Find an equation of the plane passing through points (1,9,2),(1,3,6), and (1,7,8) . Problem 71E: For the following exercises, find the equation of the sphere in standard form that satisfies the... Problem 72E: For the following exercises, find the equation of the sphere in standard form that satisfies the... Problem 73E: For the following exercises, find the equation of the sphere in standard form that satisfies the... Problem 74E: For the following exercises, find the equation of the sphere in standard form that satisfies the... Problem 75E: For the following exercises, find the center and radius of the sphere with an equation in general... Problem 76E: For the following exercises, find the center and radius of the sphere with an equation in general... Problem 77E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 78E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 79E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 80E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 81E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 82E: For the following exercises, express vector PQ with the initial paint at P and the terminal point at... Problem 83E: For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,... Problem 84E: For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,... Problem 85E: For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,... Problem 86E: For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,... Problem 87E: For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u .... Problem 88E: For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u .... Problem 89E: For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u .... Problem 90E: For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u .... Problem 91E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 92E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 93E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 94E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 95E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 96E: For the following exercises, find the unit vector in the direction of the given vector a and express... Problem 97E: Determine whether AB and PQ are equivalent vectors, where A(1,1,1),B(3,3,3),P(1,4,5), and Q(3,6,7) . Problem 98E: Determine whether the vectors AB and PQ are equivalent, where A(1,4,1),B(2,2,0),P(2,5,7), and... Problem 99E: For the following exercises, find vector u with a magnitude that is given and satisfies the given... Problem 100E: For the following exercises, find vector u with a magnitude that is given and satisfies the given... Problem 101E: For the following exercises, find vector u with a magnitude that is given and satisfies the given... Problem 102E: For the following exercises, find vector u with a magnitude that is given and satisfies the given... Problem 103E: Determine a vector of magnitude 5 in the direction of vector AB , where A(2,1,5) and B(3,4,-7) . Problem 104E: Find a vector of magnitude 2 that points in the opposite direction than vector AB , where A(1,1,1)... Problem 105E: Consider the points A(2,,0),B(0,1,), and C(1,1,), where and are negative real numbers. Find and ... Problem 106E: Consider points A(,0,0),B(0,,0), and C(,,), where and are positive real numbers. Find and such... Problem 107E: Let P(x,y,z) be a point situated at an equal distance from points A(1,1,0) and B(1,2,1) . Show that... Problem 108E: Let P(x,y,z) be a point situated at an equal distance from the origin and point A(4,1,2) . Show that... Problem 109E: The points A,B, and C are collinear (in this order) if the relation AB+BC=AC is satisfied. Show that... Problem 110E: Show that points A(1,0,1),B(0,1,1) and C(1,1,1) are not collinear. Problem 111E: [T] A force F of 50N acts on a particle in the direction of the vector OP , where P(3,4,0) . a.... Problem 112E: [T] A force F of 40N acts on a box in the direction of the vector OP , where P(1,0,2) . a. Express... Problem 113E: If F is a force that moves an object from point P1(x1,y1,z1) to another point P2(x2,y2,z2) , then... Problem 114E: A box is pulled 4 yd horizontally in the x -direction by a constant force F . Find the displacement... Problem 115E: The sum of the forces acting on an object is called the resultant or net force. All abject is said... Problem 116E: [T] Let Fk=1,k,k2,k=1,...,n be n forces acting on a particle, with n2 . a. Find the net force... Problem 117E: The force of gravity F acting on an object is given by F=mg, where m is the mass of the object... Problem 118E: A 5-kg pendant chandelier is designed such that the alabaster bowl is held by four chains of equal... Problem 119E: [T] A 30-kg block of cement is suspended by three cables of equal length that are anchored at points... Problem 120E: Two soccer players are practicing for an upcoming game. One of them runs 10m from point A to point B... Problem 121E: Let r(t)=x(t),y(t),z(t) be the position vector of a panicle at the time t[0,T], Where x,y, and z are... Problem 122E: [T] Let r(t)=t,2t2,4t2 be the position vector of a particle at time t (in seconds), where t[0,10]... format_list_bulleted