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Vector
vec(u) has an initial point
(4,8) and a terminal point
(2,4).
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 $(4,8)$ and a terminal point $(2,4)$ . $\newline$ 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

(4,8)

and a terminal point

(2,4)

.

\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

Calculate Differences: To find the magnitude of the vector $\vec{u}$ , we need to use the distance formula, which is derived from the Pythagorean theorem. The magnitude of a vector with initial point $(x_1, y_1)$ and terminal point $(x_2, y_2)$ is given by the square root of the sum of the squares of the differences in the $x$ -coordinates and $y$ -coordinates.
Square Differences: First, we calculate the differences in the x-coordinates and y-coordinates. For $\vec{u}$ , the initial point is $(4,8)$ and the terminal point is $(2,4)$ . So, the difference in the x-coordinates is $2 - 4 = -2$ , and the difference in the y-coordinates is $4 - 8 = -4$ .
Add Squares: Next, we square the differences we found in the previous step. $(-2)^2 = 4$ and $(-4)^2 = 16$ .
Find Magnitude: Now, we add the squares of the differences to find the sum: $4 + 16 = 20$ .
Find Magnitude: Now, we add the squares of the differences to find the sum: $4 + 16 = 20$ .Finally, we take the square root of the sum to find the magnitude of $\vec{u}$ . The square root of $20$ is $\sqrt{20}$ , which can be simplified to $2\sqrt{5}$ . If we want a decimal approximation, we calculate $\sqrt{20} \approx 4.47$ (rounded to the nearest hundredth).

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