Find Magnitude and Direction of a Vector

Learn how to find the magnitude (length) and direction (angle) of a vector with three detailed examples! Mario's Math Tutoring demonstrates how to use the distance formula (derived from the Pythagorean theorem) to calculate magnitude and the tangent inverse function to find the direction angle. Crucially, discover how to adjust the angle returned by your calculator to ensure it's in the correct quadrant for your vector. We'll cover vectors in component form, linear combination form, and vectors defined by initial and terminal points. In this video, you'll discover: 0:00 Introduction to Magnitude and Direction of Vectors 0:30 Example 1: Vector v = -5, 12 0:40 Graphing the Vector 1:00 Magnitude Formula: √((x)² + (y)²) (Pythagorean Theorem) 1:40 Calculating Magnitude: √((-5)² + 12²) = 13 2:10 Direction Formula: θ = tan⁻¹(y/x) 2:40 Calculator Result for tan⁻¹(12/-5) 3:00 Adjusting the Angle for the Correct Quadrant (Adding 180° for Quadrant II) 3:50 Final Magnitude and Direction for Vector v 4:10 Example 2: Vector w = 8i + 15j (Linear Combination Form) 4:30 Converting to Component Form (8, 15) and Graphing 5:00 Calculating Magnitude: √((8)² + 15²) = 17 (Pythagorean Triple!) 5:50 Calculating Direction: tan⁻¹(15/8) 6:10 Verifying the Angle is in the Correct Quadrant (Quadrant I) 6:50 Example 3: Vector AB with Initial Point A(2, 3) and Terminal Point B(-4, -5) 7:10 Graphing the Initial and Terminal Points 7:30 Finding the Vector in Component Form (Terminal - Initial) 8:00 Component Form: -6, -8 8:30 Calculating Magnitude: √((-6)² + (-8)²) = 10 9:00 Calculating Direction: tan⁻¹(-8/-6) 9:20 Calculator Result for tan⁻¹(-8/-6) 9:40 Adjusting the Angle for the Correct Quadrant (Adding 180° for Quadrant III) 10:10 Final Magnitude and Direction for Vector AB Master finding the magnitude and direction of any vector with these essential trigonometry and algebra skills! #Vectors #MagnitudeAndDirection #VectorCalculus #Precalculus #Trigonometry #MathTutorial #MathHelp ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join