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Given the vector
v has an initial point at
(4,7) and a terminal point at
(-1,7), find the exact value of
||v||.
Answer:

Given the vector $\mathbf{v}$ has an initial point at $(4,7)$ and a terminal point at $(-1,7)$ , find the exact value of $\|\mathbf{v}\|$ . $\newline$ Answer:

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Given the vector

\mathbf{v}

has an initial point at

(4,7)

and a terminal point at

(-1,7)

, find the exact value of

\|\mathbf{v}\|

.

\newline

Answer:

Identify components of vector $v$ : Identify the components of the vector $v$ . The vector $v$ is defined by its initial point $(4,7)$ and its terminal point $(-1,7)$ . To find the components of the vector, we subtract the coordinates of the initial point from the coordinates of the terminal point. $v = (\text{terminal point}) - (\text{initial point})$ $v = (-1 - 4, 7 - 7)$ $v = (-5, 0)$
Calculate magnitude of vector v: Calculate the magnitude of the vector $v$ . The magnitude of a vector (also known as the norm or length) is calculated using the formula $||v|| = \sqrt{v_x^2 + v_y^2}$ , where $v_x$ and $v_y$ are the components of the vector. $||v|| = \sqrt{(-5)^2 + (0)^2}$ $||v|| = \sqrt{25 + 0}$ $||v|| = \sqrt{25}$ $||v|| = 5$

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