Problem 123E: For the following exercises, the vectors u and v are given. Calculate the dot product uv . 123.... Problem 124E: For the following exercises, the vectors u and v are given. Calculate the dot product uv . 124.... Problem 125E: For the following exercises, the vectors u and v are given. Calculate the dot product uv . 125.... Problem 126E: For the following exercises, the vectors u and v are given. Calculate the dot product uv . 126.... Problem 127E: For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b... Problem 128E: For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b... Problem 129E: For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b... Problem 130E: For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b... Problem 131E: For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the... Problem 132E: For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the... Problem 133E: For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the... Problem 134E: For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the... Problem 135E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 136E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 137E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 138E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 139E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 140E: For the following exercises, find the measure 0f the angle between the three-dimensional vectors a... Problem 141E: For the following exercises determine whether the given vectors are orthogonal. 141. a=x,y,z,b=y,x,... Problem 142E: For the following exercises determine whether the given vectors are orthogonal. 142. a=x,x,b=y,y,... Problem 143E: For the following exercises determine whether the given vectors are orthogonal. 143.... Problem 144E: For the following exercises determine whether the given vectors are orthogonal. 144. a=ij,b=7i+2jk Problem 145E: For the following exercises determine whether the given vectors are orthogonal. 145. Find all... Problem 146E: For the following exercises determine whether the given vectors are orthogonal. 146. Find all... Problem 147E: For the following exercises determine whether the given vectors are orthogonal. 147. Determine all... Problem 148E: For the following exercises determine whether the given vectors are orthogonal. 148. Determine all... Problem 149E: For the following exercises determine whether the given vectors are orthogonal. 149. Determine the... Problem 150E: For the following exercises determine whether the given vectors are orthogonal. 150. Determine the... Problem 151E: [T] Consider the points P(4,5) and Q(5,7) . Determine vectors OP and OQ . Express the answer by... Problem 152E: [T] Consider points A(1,1),B(2,7) , and C(6,3). Determine vector BA and BC . Express the answer in... Problem 153E: Determine the measure of angle A in triangle ABC , where A(1,1,8),B(4,3,4), and C(3,1,5). Express... Problem 154E: Consider points P(3,7,2) and Q(1,1,3). Determine the angle between vectors OP and OQ . Express the... Problem 155E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 156E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 157E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 158E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 159E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 160E: For the following exercises, determine which (if any) pairs of the following vectors are orthogonal.... Problem 161E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 162E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 163E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 164E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 165E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 166E: For the following problems, the vector u is given. Find the direction cosines for the vector u .... Problem 167E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 168E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 169E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 170E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 171E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 172E: For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of... Problem 173E: A methane molecule has a carbon atom situated at the origin and four hydrogen atoms located at... Problem 174E: [T] Find the vectors that join the center of a clock to the hours 1:00,2:00, and 3:00. Assume the... Problem 175E: Find the work done by force F=5,6,2 (measured in Newtons) that moves a particle form point P(3,1,0)... Problem 176E: [T] A sled is pulled by exerting a force of 100N on a rope that makes an angle of 25 with the... Problem 177E: [T] A father is pulling his son on a sled at an angle of 20 with the horizontal with a force of 25lb... Problem 178E: [T] A car is towed using a force of 1600N . The rope used to pull the car makes an angle of 25 with... Problem 179E: [T] A boat sails north aided by a wind blowing in a direction of N30E with a magnitude of 500lb .... Problem 180E: Vector p=150,225,375 represents the price of certain models of bicycles sold by a bicycle shop.... Problem 181E: [T] Two forces F1 and F2 are represented by vectors with initial points that are at the origin. The... Problem 182E: [T] Consider r(t)=cost,sint,2t the position vector of a particle at time t[0,30] , where the... format_list_bulleted