Find the magnitude of AB (3/4)

July 13, 2026Mathematics

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Answer

\text{5}

5 steps

To find the magnitude of vector AB, we assume the given values $(3, 4)$ represent the components of the vector $\vec{AB}$ .

Identify the components of the vector $\vec{AB}$ .
The components of $\vec{AB}$ are $x=3$ and $y=4$ .
Use the formula for the magnitude of a vector.
The magnitude of a vector $\vec{v} = \begin{pmatrix} x \\ y \end{pmatrix}$ is given by:
$||\vec{v}|| = \sqrt{x^2 + y^2}$
Substitute the values of $x$ and $y$ into the formula.
$||\vec{AB}|| = \sqrt{3^2 + 4^2}$
Calculate the squares and sum them.
$||\vec{AB}|| = \sqrt{9 + 16}$ $||\vec{AB}|| = \sqrt{25}$
Find the square root.
$||\vec{AB}|| = 5$
The magnitude of AB is $\text{5}$ .

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