math226fall07pmt1

math226fall07pmt1 - 1 . Given the point P (- 3 , 2 , 4) ,...

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Unformatted text preview: 1 . Given the point P (- 3 , 2 , 4) , a) what is its distance to xy-plane? xz-plane? yz-plane? Write the equation of the sphere centered at P that touches yz-plane. b) Write the projections of P on xz-, xy-, and yz-planes. 2 . Show that the equation represents a sphere, find its radius and the center coordinates: x 2 + y 2 + z 2- 4 x + 2 y- 6 z = 0 . 3 . Use vectors to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. 4. Given two vectors ~a = h 1 , 2 , 1 i and ~ b = h- 1 , 1 , 2 i find a) the angle between ~a and ~ b ; b) the direction angles of ~a (the angles between ~a and the basis vectors ~ i, ~ j, ~ k ; c) the vector and scalar projections of ~a onto ~ b ; 5. Given three points A (1 , , 1) ,B (- 1 ,- 1 , 2) ,C (1 , 1 , 2) , a) find ~a = A ~ B and ~ b = A ~ C ; find a vector orthogonal to the plane through A,B and C ; b) write a scalar equation of the plane through the points A,B,C ; Find the distance from D (1...
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This note was uploaded on 12/16/2011 for the course MATH 226 at USC.

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