Home » Blog » Compute the norms of given vectors

Compute the norms of given vectors

by RoRi

Given vectors A = (2,-1,5), B = (-1,-2,3) and C = (1,-1,1) in \mathbb{R}^3 calculate the norms of the following vectors

  1. A+B;
  2. A - B;
  3. A + B- C;
  4. A - B + C;
  1. We compute

        \[ \lVert A+B \rVert = \sqrt{ (A+B)\cdot(A+B)} = \sqrt{(1,-3,8) \cdot (1,-3,8)} = \sqrt{74}. \]

  2. We compute

        \[ \lVert A-B \rVert = \sqrt{ (A-B) \cdot (A-B)} = \sqrt{(3,1,2) \cdot (3,1,2)} = \sqrt{14}. \]

  3. We compute

        \[ \lVert A+B-C \rVert = \sqrt{(0,-2,7) \cdot (0,-2,7)} = \sqrt{53}. \]

  4. We compute

        \[ \lVert A-B+C \rVert = \sqrt{(4,0,3) \cdot (4,0,3)} = \sqrt{25} = 5. \]

One comment

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):