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Find the unit vectors that are parallel to the tangent line to the parabola $ y = x^2 $ at the point $ (2, 4) $.

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01:21

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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01:22

for the given problem, we want to find the two unit vectors that are parallel to the tangent line of the prob. The problem Y equals x squared At the .24. So we're gonna have Y equals X squared. Um and then if we look at the .24, we know that the slope of the line at this point is going to be Um four. So since the slope is for, we know that um the UAE over the X. Component is going to be for, so what this looks like since it's a unit vector is We just need to find the magnitude. So since we have one component that's one and one that's four, we see the magnitude would be route 17. So our unit factors can be won over route 17 Or over Route 17. And then if we wanted a second vector that's parallel, that's a unit vector, we would just look at the negative form of that and it would be the same thing.

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