11. Find the angle between the planes. (a) 2r-y+:-5 andr+y=:= 1. (b) z-y-2:-10 and z-y-2: -5....

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11. Find the angle between the planes. (a) 2r-y+:-5 andr+y=:= 1. (b) z-y-2:-10 and z-y-2: -5. 12. Find the Cartesian equation of the line passing through P(2, 3, 1) and parallel to the line of intersection of the planes x+2y-32-4 and z-2y+z=0. 13. (a) Find the distance from the point (1,-1, 2) to the line x+2_1-12 (b) Find the distance from the point R(2,-1, 5) to the line passing through P(2, 1, 3) and Q(1,-1, 4). 14. Let A(1, 2, 3), B(1,-1, 0), C(2, 4, 7), and D(0, 1, 1). Find (a) the normal vector to the plane ABC, (b) the parametric equation of the line perpendicular to ABC and passes through B. (e) the equation of the plane ABD, (d) the acute angle between planes ABD and ABC. 15. Given the equation of two lines; (₁ : 2=2+ 3t, y=-4+t and -1-t, ₂: x=-1+28, y=-4+8 and 2--2-28. Find (a) the point of intersection between the lines ₁ and ₂. (b) the acute angle between the lines ₁ and ₂ at the point of intersection. 16. Find the shortest distance from the point (5,2,-1) to the line 17. Find the shortest distance between the following lines. 1-9 y-9 -14 3 Am 1. 18. Find the angle between the plane z+y+z=2 and the line z=1+1, y=2+2t, and ==3+2t. 11. Find the angle between the planes. (a) 2r-y+:-5 andr+y=:= 1. (b) z-y-2:-10 and z-y-2: -5. 12. Find the Cartesian equation of the line passing through P(2, 3, 1) and parallel to the line of intersection of the planes x+2y-32-4 and z-2y+z=0. 13. (a) Find the distance from the point (1,-1, 2) to the line x+2_1-12 (b) Find the distance from the point R(2,-1, 5) to the line passing through P(2, 1, 3) and Q(1,-1, 4). 14. Let A(1, 2, 3), B(1,-1, 0), C(2, 4, 7), and D(0, 1, 1). Find (a) the normal vector to the plane ABC, (b) the parametric equation of the line perpendicular to ABC and passes through B. (e) the equation of the plane ABD, (d) the acute angle between planes ABD and ABC. 15. Given the equation of two lines; (₁ : 2=2+ 3t, y=-4+t and -1-t, ₂: x=-1+28, y=-4+8 and 2--2-28. Find (a) the point of intersection between the lines ₁ and ₂. (b) the acute angle between the lines ₁ and ₂ at the point of intersection. 16. Find the shortest distance from the point (5,2,-1) to the line 17. Find the shortest distance between the following lines. 1-9 y-9 -14 3 Am 1. 18. Find the angle between the plane z+y+z=2 and the line z=1+1, y=2+2t, and ==3+2t.

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