Question

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

Answer 1

$A=\left( 2,3,-1 \right) ,B=\left( 1,-1,2 \right) ,C=\left( 3,4,1 \right) \\a:\\A+2B=\left( 2+2,3-2,-1+4 \right) =\left( 4,1,3 \right) \\b:\\A-B+2C=\left( 2-1+6,3+1+8,-1-2+2 \right) =\left( 7,12,-1 \right) \\\left| A-B+2C \right|=\sqrt{7^2+12^2+1^2}=\sqrt{194}\\c:\\A-B+C+3D=0\Rightarrow \\\Rightarrow D=\frac{1}{3}\left( B-A-C \right) =\frac{1}{3}\left( 1-2-3,-1-3-4,2+1-1 \right) =\\=\left( -\frac{4}{3},-\frac{8}{3},\frac{2}{3} \right)$