Given the vector vv has an initial point at left parenthesis, minus, 2, comma, 5, right parenthesis(−2,5) and a terminal point at left parenthesis, minus, 2, comma, 1, right parenthesis(−2,1), find the exact value of \lVert, v, \lVert, .∥v∥.

The vector \(\mathbf{v}\) is given by its initial point \((-2, 5)\) and terminal point \((-2, 1)\). To find the magnitude (or norm) \(\|\mathbf{v}\|\) of the vector, we first calculate the vector's components by subtracting the initial point from the terminal point.

\[
\mathbf{v} = \left( -2 - (-2), 1 - 5 \right) = \left( 0, -4 \right)
\]

Now, the magnitude of the vector \(\mathbf{v} = (0, -4)\) is given by the formula:

\[
\|\mathbf{v}\| = \sqrt{(0)^2 + (-4)^2} = \sqrt{0 + 16} = \sqrt{16} = 4
\]

Thus, the exact value of \(\|\mathbf{v}\|\) is 4.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the formula for finding the magnitude of a vector in 3 dimensions?
2. How do you calculate the direction of a vector?
3. How would the magnitude of the vector change if both components were negative?
4. What does the magnitude of a vector represent geometrically?
5. Can a vector have a negative magnitude?

**Tip:** The magnitude of a vector is always a non-negative value since it's the length of the vector in space.

Given the vector v has an initial point at (-2, 5) and a terminal point at (-2, 1), find the exact value of ∥v∥.

Learn how to calculate the magnitude of a vector with initial point (-2, 5) and terminal point (-2, 1). This problem explores vector geometry and the use of the magnitude formula based on the Pythagorean theorem. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation