Vectors in space

# Vectors in space - 2(z c 2 = d(x y z(a b c = r or(x 2 2(y 2...

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Section 10.2 Vectors in Space Find a unit vector in the same direction as ( 1, -2, 8 ). First, we find the magnitude of the vector: (1, -2, 8) = 1 2 + (-2) 2 + 8 2 = 69 . A unit vector having the same direction as ( 1, -2, 8 ) is given by u = 1 69 ( 1, -2, 8 ) = ( 1 69 , -2 69 , 8 69 ) . See page 802 for more details. Find the equation of the sphere of radius 6 centered at the point (2, 2, 1). The sphere consists of all points (x, y, z) whose distance from (a, b, c) is 6. This says that (x - a) 2 + (y - b)
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Unformatted text preview: 2 + (z - c) 2 = d{(x, y, z),(a, b, c)} = r, or (x - 2) 2 + (y - 2) 2 + (z - 1) 2 = d{(x,y,z),(2,2,1)} = 6. Squaring both sides gives us the standard form of the equation of a sphere: (x - 2) 2 + (y - 2) 2 + (z - 1) 2 = 36. See page 802 for more details. Find the distance between the points (2, -4, 3) and (6, 1, -2). From (2.2), we have d{(2,-4,3) , (6,1,-2)} = (6-2) 2 + (1-(-4)) 2 + (-2-3) 2 = 4 2 + 5 2 + (-5) 2 = 66 . See page 800 for more details....
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## This note was uploaded on 01/19/2011 for the course MATH 2730 taught by Professor Noname during the Spring '10 term at Kalamazoo Valley Community College.

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