# Mathematics

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Write an equation in both rectangular and polar form for the line with slope -1 through (3, -1 )
[Calculus]
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Write an equation in both rectangular and polar form for the horizontal line through (2, 5 )
[Calculus]
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Write an equation in both rectangular and polar form for the vertical line through (-3, 0 )
[Calculus]
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Find a vector that has the same direction as 6i - 3j and is (a) four times its length; (b) one third its length
[Calculus]
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Given a = 2i + 3j, b = 3i + 5j, and c = 8i + 11j express c in the form ra + sb where r and s are scalars
[Calculus]
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Given a = 5i + 9j and b =12i - 10j, determine whether or not a and b are perpendicular
[Calculus]
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Find (to the nearest degree) each angle of the triangle with vertices A(1, 2, 3 ), B(4, 1, 3 ), and C(1,2, 6 )
[Calculus]
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Find (to the nearest degree) each angle of the triangle with vertices A(1, 1, 1 ), B(0, 0, 3 ), and C(4, -1, -3 )
[Calculus]
(3)

Given the points A(1, 3, -4 ), B(3, 8, 6 ), C(-1, 2, -4 ) and D(-4, 4, -5 ), determine whether or not the points are coplanar. If not, find the volume of the pyramid formed with these points as its vertices
[Calculus]
(3)

Given the points A(3, 1, 2 ), B(4, 2, 1 ), C(5, 4, 0 ) and D(7, 6, 6 ), determine whether or not the points are coplanar. If not, find the volume of the pyramid formed with these points as its vertices
[Calculus]
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Write an equation of the plane that contains the point P(1, 3, 5 ) and the line L: x = 4t, y = 6 + 5t, z = 3 - 2t
[Calculus]
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Find an equation of the plane through the points P(1, 3, 5 ), Q(2, 4, 6 ), and R(-5, -2, -3 )
[Calculus]
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Find an equation of the plane with normal vector n = 3i - 2j + k that passes through P(6, 2, -5 )
[Calculus]
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Find an equation of the plane that passes through the points P(1, 2, 3 ) and Q(-1, 2, -3 ) and is parallel to line of intersection of the planes x + y + z = 1 and 4x - 2y - z = 5
[Calculus]
(3)

Determine whether the line L: x = 5 - 4t, y = 16 + 6t, z = 2 + 5t and the plane 4x + y + 2z = 10 intersect or are parallel. If the intersect, find the point of intersection
[Calculus]
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A particle moves in space. Its position vector at time t is r(t) [] ti ε j sin t ε k cos t. Find the velocity and acceleration vectors at time t [] 0
[Calculus]
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A particle moves in space. Its path is parametrized by the vector-valued function r(t) [] 2i cos t ε 2j sin t ε tk. Find the velocity and acceleration vectors
[Calculus]
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Find the great circle distance in miles from New York (latitude 40.75[] North, longitude 74[] West) to Atlanta (latitude 33.75[] North, longitude 84.4[] West)
[Calculus]
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Find the volume of the solid bounded below by z = -2 + x + y and above by z = 5, that lies above the plane region inside r = 1
[Calculus]
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