# Linear Dependence and Coplanarity Unit Assignment 2.docx -...

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Linear Dependence and Coplanarity Unit Assignment 1. a. (3,0,0) b. (0,3,2) c. (2,0,0) d. (0,0,0) e. (4,5,5) 2. A ( 4,7,7 ) B ( 1,6,5 ) C ( 2,9,8 ) . AB = ( 4 1 ) 2 +( 7 6 ) 2 +( 7 5 ) 2 . ¿ 14 . BC = ( 1 + 2 ) 2 +( 6 9 ) 2 +( 5 8 ) 2 . ¿ 27 . CA = (− 2 4 ) 2 +( 9 7 ) 2 +( 8 7 ) 2 . ¿ 41 41 ¿ ¿ Here A B 2 + BC 2 = 14 + 27 = 41 = ¿ ABCΔ isa ¿ AngleTriangle 3. A ( 2,4,5 ) B ( 4,5 , 3 ) C ( 1 , 1,6 ) There are 3 possible solutions becausellegram is 3 D . A = ( 2 ^ i + 4 ^ j + 5 ^ k ) then . D 1 =( B + C A ) . B = ( 4 ^ i + 5 ^ j 3 ^ k ) . D 2 =( A + C B ) . C = ( ^ i ^ j + 6 ^ k ) . D 3 =( A + B C ) D 1 = B + C A = 7 ^ i + 0 ^ j 2 ^ k D 1 =( 7,0 , 2 )
. D 2 = A + C B =− 5 ^ i 2 ^ j + 14 ^ k D 2 =(− 5 , 2,14 ) . D 3 = A + B C = ^ i + 10 ^ j 4 ^ k D 3 =( 1,10 , 4 ) 4. A ( 2 , 1 ,z ) ,B ( 2,4,3 ) ,C ( 10 , y , 1 ) . AB =( 2 (− 2 ) , 4 −( 1 ) , 3 z ) . AB =( 4,5,3 z ) . BC =( 10 (− 2 ) , y — (− 1 ) , 1 z ) . BC =( 12, y + 1, 1 z ) s AB = BC s ( 4,5,3 z ) =( 12 , y + 1, 1 z ) 3 ( 4,5,3 z ) =( 12 , y + 1, 1 z ) ( 12,15,9 3 z ) =( 12 , y + 1, 1 z ) 15 = y + 1 , 9 3 z =− 1 z 14 = y , 9 + 1 =− z + 3 z 10 = 2 z 5 = z 5. . Directionangleof a vectormeansthe angle whichavector makeswith positive x axis y θ ( x, y v x
. Vector vhas directionangle = θ,where v = | v | cosθ ^ i + | v | sin ϑ ^ i . Where | v | isthe magnitude of vector v a. . cos = a 2 a 2 + b 2 + c 2 . cosβ = b 2 a 2 + b 2 + c 2 .