An equation for the tangent plane to the sphere and which

Question

1. An equation for the tangent plane to the sphere

x² + y² + z² - 2x - 4y + 3z = 13 at the point P(3, 4, -5) is

a)   x + y + z = 2                   d)    x - 2y - 2z + 12 = 0

b)   10x + 3y - 3z = 57        e)    3x + 4y - 5z --- 50

c)   4x + 4y - 7z - 63

2. The line which passes through the point (5, -8, 5) and which is perpendicular to the plane 2x - y + 4z + 4 = 0 intersects that plane at the point

a) (1, 10, 1)

b) (1, -6, -3)

c) (-1, -2, -1)

d) (-1, 10, 4)

e) (8, 4, -1)

3. Let A^-> and B^-> be vectors in space. Suppose A^-> . B^-> = 3 and A^-> x B^->= (- √2, 3, -4). The geometric interpretations of A-^> . B^->and A x B in terms of ||A^->||, ||B^->||, and the angle θ between these vectors can be used to solve for θ by forming the ratio ||A^-> x B^->|| / A^-> .B^->. In this way the angle θ in degrees is found to be

a) 30°      b) 45^o      c) 60°       d) 90°    e) 0^o