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1. [-/6 Points] DETAILS LARCALC12 11.1.041. Find the following. U = (1 , 5 , V = (5 , 8 ) (a) |lull ( c ) u (d) (e) V utv ( f ) u + vil10. [-/1 Points] DETAILS LARCALC12 11.5.044. Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to x - 1 z+ 5 (5, 4, 4) =y+4 =. 8 -511. [-/1 Points] DETAILS LARCALC12 11.5.042. Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to (0, 5, 0) n = -6i + 6k12. [-/4 Points] DETAILS LARCALC12 11.6.030. MY NOTES ASK YOUR TEACHER PRACTICE AN The four figures are graphs of the quadratic surface z = x + y". Match each of the four graphs with the point in space from which the paraboloid is viewed. The four points are (0, 0, 20), (0, 20, 0), (20, 0, 0), and (10, 10, 20). (a) O (0, 0, 20) (0, 20, 0) O (20, 0, 0) (10, 10, 20) (b) O (0, 0, 20) (0, 20, 0) (20, 0, 0) (10, 10, 20) (c) 2. [-/1 Points] DETAILS LARCALC12 11.1.055. MY NOTES Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. | |u |1 = 7, 01 =9 | |v|1 = 1, 01 =7 u +v=3. [-I4 Points] DETAILS LARCALC12 11.2.049. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The initial and terminal points of a vector v are given. Initial point: (1, 3, 4) Terminal point: (4, 4, 5) (a) Sketch the directed line segment. ]O 10 10 10 -10 -5 10 -10 -5 -5 -10 -5 5 5 -5 5 -10 10 5 5 -10 X 10 X 10 O O 10 10 -10 10 -10 5 -5 -5 -10 -U -5 5 -5 5 10 5 5 -10 10 X 10 X 10(b) Find the component form of the vector. (c) Write the vector using standard unit vector notation. (d) Sketch the vector with its initial point at the origin. WebAssign Plot 4. [-I3 Points] DETAILS LARCALC12 11.2.051. MY NOTES | ASK YOUR T Find the component form and magnitude of the vector v with the given initial and terminal points. Then find a unit vector in the direction of v. Initial point: (3, 6, 0) Terminal point: (4, 1, 2) . [-11 Points] DETAILS LARCALC12 11.3.024. Determine whether u and v are orthogonal, parallel, or neither. u = 3i + 8j k v = 3i +j k parallel orthogonal neither 6. [I6 Points] DETAILS LARCALC1211.3.031. MY NOTES | ASK YOUR TEACH 2 Find the direction cosines and angles of u and show that cos 0: + cos2 3 + cos2 y = 1. (Round your answers for the angles to four decimal places.) u=i+2j+2k cosoz: => dz rad cos/3: => x rad cosy: = y: rad 9. [-11 Points] DETAILS LARCALC12 11.5.039. Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to (3! 5r 9) n = j S