vector - VECTORS, DOT PRODUCT O. Knill, Math21a HOMEWORK:...

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Unformatted text preview: VECTORS, DOT PRODUCT O. Knill, Math21a HOMEWORK: Section 11.1: 34,36, Section 11.2: 76, Section 11.3: 20, 62, Due Friday, September 29 VECTORS. Two points P = ( x 1 , y 1 ), Q = ( x 2 , y 2 ) in the plane define a vector vectorv = ( x 2 x 1 , y 2 y 1 ) . It points from P to Q and we can write P + vectorv = Q . COMPONENTS. Points P in space are in one to one correspondence to vectors pointing from 0 to P . The numbers vectorv i in a vector vectorv = ( v 1 , v 2 ) are also called components or of the vector. REMARKS: vectors can be drawn everywhere in the plane. If a vector starts at the origin O , then the vector vectorv = ( v 1 , v 2 ) points to the point ( v 1 , v 2 ) . Thats is why one can identify points P = ( a, b ) with vectors vectorv = ( a, b ) . Two vectors which can be translated into each other are considered equal . They have the same components. ADDITION, SUBTRACTION AND SCALAR MULTIPLICATION. x y u v u+v x y u v u-v x y u 3 u vectoru + vectorv = ( u 1 , u 2 ) + ( v 1 , v 2 ) = ( u 1 + v 1 , u 2 + v 2 ) vectoru vectorv = ( u 1 , u 2 ) ( v 1 , v 2 ) = ( u 1 v 1 , u 2 v 2 ) vectoru = ( u 1 , u 2 ) = ( u 1 , u 2 ) BASIS VECTORS. The vectors vector i = ( 1 , ) , vector j = ( , 1 ) are called standard basis vectors in the plane. In space, one has the basis vectors vector i = ( 1 , , ) , vector j = ( , 1 , ) , vector k = ( , , 1 ) . Every vector vectorv = ( v 1 , v 2 ) in the plane can be written as vectorv = v 1 vector i + v 2 vector j . Every vector vectorv = ( v 1 , v 2 , v 3 ) in space can be written as vectorv = v 1...
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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