Answer to Question #318674 in Analytic Geometry for Agenda

Question #318674

Given that A = 2i + 3j - k, B = i - j +2k and C = 3i + 4j + k find:



a) A+2B



b) |A- B+2C|



c) D such that A - B + C 3D = 0





1
Expert's answer
2022-03-29T08:54:15-0400

A=(2,3,1),B=(1,1,2),C=(3,4,1)a:A+2B=(2+2,32,1+4)=(4,1,3)b:AB+2C=(21+6,3+1+8,12+2)=(7,12,1)AB+2C=72+122+12=194c:AB+C+3D=0D=13(BAC)=13(123,134,2+11)==(43,83,23)A=\left( 2,3,-1 \right) ,B=\left( 1,-1,2 \right) ,C=\left( 3,4,1 \right) \\a:\\A+2B=\left( 2+2,3-2,-1+4 \right) =\left( 4,1,3 \right) \\b:\\A-B+2C=\left( 2-1+6,3+1+8,-1-2+2 \right) =\left( 7,12,-1 \right) \\\left| A-B+2C \right|=\sqrt{7^2+12^2+1^2}=\sqrt{194}\\c:\\A-B+C+3D=0\Rightarrow \\\Rightarrow D=\frac{1}{3}\left( B-A-C \right) =\frac{1}{3}\left( 1-2-3,-1-3-4,2+1-1 \right) =\\=\left( -\frac{4}{3},-\frac{8}{3},\frac{2}{3} \right)


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