Find an equation of the sphere with center (1, 12, 6) and radius 10. (x1)'2+ (y+12)2+(z6)2:100 / Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.) intersection with xy-plane 64 intersection with xz-plane DNE intersection with yz-plane 99 Find a unit vector that has the same direction as the given vector. 4i+3jk PM 3 i (-11%: m m m Find the unit vectors that are parallel to the tangent line to the parabola y = x- at the point (6, 36). 1 12 smaller i-component 145 145 X -1 12 larger i-component it V 145 V 145 XFind two unit vectors that make an angle of 60 with v = 8i + 6j. (Round your answers to four decimal places.) smaller i-component larger i-component Find the scalar and vector projections of b onto a. a=(1,6), b=(3,5) scalar projection of b onto a vector projection of b onto a (14,12) Find the scalar and vector projections of b onto a. a = (1,4, 8}, b =(14,1,2) scalar projection of b onto a 6 vector projection of b onto a (1543) llll llJll Determine whether the planes are parallel, perpendicular, or neither: X+4yz=4, 4x4y+z=1 0 parallel O perpendicular neither / If neither, find the angle between them. (Use degrees and round to one decimal place. If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.) 122.2 0 Use traces to sketch the surface. (If an answer does not exist, enter DNE. Seiect Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) 2x2+y+222=0 (Write an equation for the cross section at z = 0 using x and y.) 2x2 +J: : 0 / . . . _ -) 0 (Write an equation for the cross section at y = 2 usmg x and z.) x- + Z' : .1