100hw1

100hw1 - A 6(11.5 22 Find the parametric equation of the line through the origin that is parallel to the line given by x = 2 t y =-1 t z = 2 7(11.5

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Math 100 Homework 1 fall 2010 due 15/9 1. (11.1, 24) Describe the surface whose equation is given by x 2 + y 2 + z 2 - y = 0 . 2. (11.3, 22) Find the acute angle formed by two diagonals of a cube. 3. (11.3, 28) Determine if it is true that for any vectors a , b , c such that a 6 = 0 and a · b = a · c , then b = c . 4. (11.4, 14) Determine if it is true that for any three vectors a , b , c , a × ( b × c ) = ( a × b ) × c. 5. (11.4, 30) Show that in the 3-space the distance d from a point P to the line through points A and B can be expressed as d = || -→ AP × --→ AB || || --→ AB || . Where --→ AB stands for the vector representing the point B minus the vector representing the point
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Unformatted text preview: A . 6. (11.5, 22) Find the parametric equation of the line through the origin that is parallel to the line given by x = 2 t , y =-1 + t , z = 2. 7. (11.5, 52) Let L be the line that passes through the point ( x , y , z ) and is parallel to v = ( a, b, c ), where a , b , c are nonzero. Show that a point ( x, y, z ) lies on the line L if and only if x-x a = y-y b = z-z c . These equations, which are called the symmetric equations of L , provides a nonparametric representation of L . 1...
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This note was uploaded on 12/25/2011 for the course MATH 101 taught by Professor Ching during the Spring '11 term at HKU.

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