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For two vectors U and A The vector component of U along A is give.pdf

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For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40) Solution For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40).

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For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40) Solution For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40)

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For two vectors U and A The vector component of U along A is give.pdf

  • 1. For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40) Solution For two vectors U and A : The vector component of U along A is given as { (U.A)/||A||^2 } A U =(14,7,7,14) ; A =(4, -4 ,2 , -2) U.A = 14.4 -7.4 +7.2 -14.2 = 56-28+14-28 =14 ||A||^2 = ( 4^2 +4^2+2^2 +2^2) =(16+16+4+4)= (40) vector component of U along A is given as = (14/ 40)(A) =(14/ 40){4,-4,2,-2} =(56/40 ,-56/40, 28/40 , -28/40) vector component of U orthogonal to A is given as = vector U - vector component of U along A = (14,7,7,14) -(56/40 ,-56/40, 28/40 , -28/40) =(504/40 ,336/40 ,252/40 ,588/40)