What is magnitude of vector

July 8, 2026Mathematics

ScanSolve AI Answer

July 8, 2026

Answer

\sqrt{v_1^2 + v_2^2 + \dots + v_n^2} $$

The magnitude of a vector is its length. It is a non-negative scalar value. For a vector $\vec{v} = \langle v_1, v_2, \dots, v_n \rangle$ in $n$ -dimensional space, its magnitude, denoted as $||\vec{v}||$ , is calculated using the Pythagorean theorem:

$||\vec{v}|| = \sqrt{v_1^2 + v_2^2 + \dots + v_n^2}$

For example, the magnitude of the 2D vector $\vec{a} = \langle 3, 4 \rangle$ is:

$||\vec{a}|| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

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The magnitude of a vector is its length. It is a non-negative scalar value.

Asked on July 8, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on July 8, 2026

The magnitude of a vector is its length. It is a non-negative scalar value. For a vector v = v_1, v_2, , v_n in n -dimensional space, its magnitude, denoted as ||v|| , is calculated using the Pythagorean theorem: ||v|| = sqrt(v_1^2 + v_2^2 + + v_n^2) For example, the magnitude of the 2D vector a = 3, 4 is: ||a|| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 What's next? 📸