Math Problem Statement

Soit un repère orthonormé (O; i, j), et u(−3; 2). Déterminer la norme du vecteur u.

Solution

The task is asking for the determination of the norm (or magnitude) of a vector u\mathbf{u}, given its components in a coordinate system.

From the image, we see the vector u=(3,2)\mathbf{u} = (-3, 2), and we are working in an orthonormal reference frame, meaning the vectors i\mathbf{i} and j\mathbf{j} are orthogonal and of unit length.

To find the norm of vector u=(3,2)\mathbf{u} = (-3, 2), we use the formula for the norm of a 2D vector:

u=(3)2+22\|\mathbf{u}\| = \sqrt{(-3)^2 + 2^2}

Let's compute this:

u=9+4=13\|\mathbf{u}\| = \sqrt{9 + 4} = \sqrt{13}

Thus, the norm of vector u\mathbf{u} is 13\sqrt{13}.

Would you like more details on how this formula is derived, or do you have any questions? Here are a few related questions that might help expand on this concept:

  1. How is the norm of a vector used in various applications?
  2. How do you compute the norm of a 3D vector?
  3. What is the relationship between the direction of a vector and its norm?
  4. Can the norm of a vector be negative?
  5. How do you find the unit vector corresponding to a given vector?

Tip: Always check that you're using the correct component values (i.e., xx and yy coordinates) when applying the formula for vector magnitude.

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Math Problem Analysis

Mathematical Concepts

Vector Norm
Coordinate Systems
Orthogonal Vectors

Formulas

|u| = √(x^2 + y^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-11