Given 𝑎⃗  = <4, 5, 6> 

|𝑎⃗ |=

The magnitude (or length) of the vector \(\mathbf{a} = \langle 4, 5, 6 \rangle\) can be found using the formula for the magnitude of a vector in three-dimensional space:

\[
||\mathbf{a}|| = \sqrt{a_1^2 + a_2^2 + a_3^2}
\]

Substituting the components of the vector \(\mathbf{a} = \langle 4, 5, 6 \rangle\):

\[
||\mathbf{a}|| = \sqrt{4^2 + 5^2 + 6^2}
\]

Calculating each term:

\[
||\mathbf{a}|| = \sqrt{16 + 25 + 36} = \sqrt{77}
\]

So, the magnitude \(||\mathbf{a}||\) is \(\sqrt{77}\).

Would you like more details or have any questions? Here are some related questions you might consider:

1. How do you find the magnitude of a vector in two-dimensional space?
2. How would you compute the magnitude of a vector given its initial and terminal points?
3. What is the unit vector corresponding to \(\mathbf{a} = \langle 4, 5, 6 \rangle\)?
4. How does the magnitude of a vector relate to its components?
5. What is the geometric significance of the magnitude of a vector?

**Tip:** When calculating the magnitude of a vector, always square each component individually, sum them, and then take the square root of the total.

Learn how to calculate the magnitude of the vector <4, 5, 6> in three-dimensional space. This problem covers vectors and the magnitude formula, suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation