1. For each of the following sets of vectors determine the projection of v onto w....

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1. For each of the following sets of vectors determine the projection of v onto w. (a) v = (1,2,3), w = (1, 2, 1) (b) v = (2,0, -3), w = (5, 1,8) 2. For each of Questions la and 1b, determine v. 3. Determine the smallest angle formed by each of the following sets of lines in R. (a) r(t) = (2,6, -9) + t(6, 2, 8) and r(s) = (7, 1, 0) + s(-3, -6, 1). (b) r(t) = (4, 3, 10) + t(4, 9, 5) and r(s) = (3,3,3)+ s(4, 1, 9). 4. The points P = (1, 2, 3), Q = (4, 2, 3), R = (3, 5, 2) and S = (2, 5, 2) form a trapezoid in 3D space. Answer the following questions. (a) Sketch the trapezoid in 3D space. (b) Find the equation of the plane on which the trapezoid lies. (c) Using cross products, determine the area of the trapezoid PQRS. 5. Determine the intersection of the planes 3x 7y + 2z = 10 and -x+6y + 3z = 12. 1. For each of the following sets of vectors determine the projection of v onto w. (a) v = (1,2,3), w = (1, 2, 1) (b) v = (2,0, -3), w = (5, 1,8) 2. For each of Questions la and 1b, determine v. 3. Determine the smallest angle formed by each of the following sets of lines in R. (a) r(t) = (2,6, -9) + t(6, 2, 8) and r(s) = (7, 1, 0) + s(-3, -6, 1). (b) r(t) = (4, 3, 10) + t(4, 9, 5) and r(s) = (3,3,3)+ s(4, 1, 9). 4. The points P = (1, 2, 3), Q = (4, 2, 3), R = (3, 5, 2) and S = (2, 5, 2) form a trapezoid in 3D space. Answer the following questions. (a) Sketch the trapezoid in 3D space. (b) Find the equation of the plane on which the trapezoid lies. (c) Using cross products, determine the area of the trapezoid PQRS. 5. Determine the intersection of the planes 3x 7y + 2z = 10 and -x+6y + 3z = 12.