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If $ v $ lies in the first quadrant and makes an angle $ \frac{\pi}{3} $ with the positive x-axis and $ \mid v \mid = 4 $, find $ v $ in component form.

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00:44

Alan Ghazarians

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Missouri State University

Campbell University

Harvey Mudd College

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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$$\begin{array}{l}{\text {…

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If v lies in the first qua…

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Find the component form of…

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The initial point of a vec…

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02:51

So for the given problem, If v lies in the first quadrant and makes an angle of pi over three with the positive X. Axis and the magnitude of the is four, we want to find V. In component form. So one way we could look at this is recognizing that pi over three because degrees. So how we're going to look at this is we could do um V the magnitude times code sign. What are vector is going to look like? Is V co Cynthia to the sign painter because we're creating a right triangle. Um and if we do this, we'll be able to see that there's going to be an X. Component, that's vico, santa, ana Y component, that's be signed data. So what we're gonna end up having is four times co sign of 60 that's going to give us to And then four times co sign Are four times seven or 60 that's going to give us to route three.

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