6. [-/1 Points] DETAILS LARCALC11 11.3.031. Find the direction cosines and angles of u and show that cos2 a + cos2 [n' + cos2 y = 1. (Round your answers for the angles to four decimal places.) u=i+8j+4k cos a = => ax rad cos ,B = 2 [32 rad cos y = => y z rad Need Help? 7. [-/1 Points] DETAILS LARCALC11 11.3.039. Consider the following. u=2i+7j, v=3i+9j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v. 8. [-11 Points] LARCALC11 11.3.054. ASK YOUR TEACHER PRACTICE ANOTHER Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not unique. Enter your answer as a comma-separated list of vectors.) u = (5, 4, 7) Need Help? 9. [-/1 Points] LARCALC11 11.3.057. ASK YOUR TEACHER PRACTICE ANOTHER A 34,000-pound truck is parked on a 10" slope (see figure). Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill and the force perpendicular to the hill. (Round your answers to one decimal place.) Weight = 34,000 lb (3) Find the force required to keep the truck from rolling down the hill. |b (b) Find the force perpendicular to the hill. lb 10. [-/1 Points] DETAILS LARCALC11 11.3.061. MY NOTES ASK YOUR TEACHER A car is towed using a force of 1300 newtons. The chain used to pull the car makes a 270 angle with the horizontal. Find the work done in towing the car 6 kilometers. (Round your answer to one decimal place.) km-N Need Help? Read It Watch It 11. [-/1 Points] DETAILS LARCALC11 11.3.065. MY NOTES Consider the following. y1 = x, y2 = x1/3 (a) Find all points of intersection of the graphs of the two equations. Point A (x, y) = ( ) (smaller x-value) Point B (x, y) = ( ) (larger x-value) (b) Find the unit tangent vectors to each curve at their points of intersection. unit vector tangent to y1 at Point A = + unit vector tangent to y2 at Point A = + unit vector tangent to y1 at Point B = unit vector tangent to y2 at Point B = (c) Find the angles (0 s 0 s 900) between the curves at their points of intersection. Point A Point B