### Educational Website Content---**Question 15**If a vector has an initial point of \((-1, -3)\) and a terminal point of \((6, 7)\), what is the magnitude and direction of the vector? Round your answers to the nearest hundredth.**Show your work****Note:** If you would rather show your work on a separate sheet of paper, you may upload your work in Question 16.---**Detailed Explanation:**To find the magnitude and direction of the vector, follow these steps:1. **Calculate the components of the vector:** - Let the initial point be \(A(-1, -3)\) and the terminal point be \(B(6, 7)\). - The components of the vector \(\vec{AB}\) can be found using: \[ \vec{AB} = (x_2 - x_1, y_2 - y_1) \] where \(A(x_1, y_1)\) and \(B(x_2, y_2)\). - Substituting the given points: \[ \vec{AB} = (6 - (-1), 7 - (-3)) = (7, 10) \]2. **Find the magnitude of the vector:** - Use the formula for the magnitude of a vector: \[ |\vec{AB}| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] - Substituting the values: \[ |\vec{AB}| = \sqrt{(7)^2 + (10)^2} = \sqrt{49 + 100} = \sqrt{149} \approx 12.21 \] - The magnitude of the vector is approximately **12.21**.3. **Find the direction (angle) of the vector:** - To find the direction of the vector, calculate the angle \(\theta\) with respect to the positive x-axis using: \[ \theta = \tan^{-1}\left(\frac{y_2 - y_1}{x_2 - x_1}\right) \] - Substituting the values: \[ \theta = \tan^{-1}\left(\frac

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SKETCHPAD Question 15 If a vector has an initial point of (-1, -3) and a terminal point of (6, 7), what is the magni- tude and direction of the vector? Round your answers to the nearest hundredth. Show your work Note: If you would rather show your work on a separate sheet of paper, you may upload your work in Question 16.

SKETCHPAD Question 15 If a vector has an initial point of (-1, -3) and a terminal point of (6, 7), what is the magni- tude and direction of the vector? Round your answers to the nearest hundredth. Show your work Note: If you would rather show your work on a separate sheet of paper, you may upload your work in Question 16.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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