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Vector
vec(u) has an initial point
(5,1) and a terminal point
(-3,4).
Find the magnitude of
vec(u).
Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.

|| vec(u)||=◻

Vector $\vec{u}$ has an initial point $(5,1)$ and a terminal point $(-3,4)$ . $\newline$ Find the magnitude of $\vec{u}$ . $\newline$ Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth. $\newline$ $\|\vec{u}\|=\square$

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Evaluate piecewise-defined functions

Full solution

Q. Vector

\vec{u}

has an initial point

(5,1)

and a terminal point

(-3,4)

.

\newline

Find the magnitude of

\vec{u}

.

\newline

Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.

\newline

\|\vec{u}\|=\square

Use Distance Formula: To find the magnitude of the vector $\vec{u}$ , we need to use the distance formula, which is derived from the Pythagorean theorem. The distance formula for a vector with initial point $(x_1, y_1)$ and terminal point $(x_2, y_2)$ is: $\newline$ $||\vec{u}|| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute Given Points: Substitute the given points into the distance formula: $\newline$ Initial point $(x_1, y_1) = (5, 1)$ $\newline$ Terminal point $(x_2, y_2) = (-3, 4)$ $\newline$ $||\vec{u}|| = \sqrt{(-3 - 5)^2 + (4 - 1)^2}$
Calculate Differences: Calculate the differences: $\newline$ $(-3 - 5) = -8$ $\newline$ $(4 - 1) = 3$ $\newline$ Now, square these differences: $\newline$ $(-8)^2 = 64$ $\newline$ $(3)^2 = 9$
Add Squares: Add the squares of the differences: $64 + 9 = 73$
Find Magnitude: Take the square root of the sum to find the magnitude: $\newline$ $||\vec{u}|| = \sqrt{73}$

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