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Find the vector that has the same direction as $ \langle 6, 2, -3 \rangle $ but has length 4.

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01:01

Alan Ghazarians

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Campbell University

Oregon State University

University of Nottingham

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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doctor we have here, we wanted to Have the same direction as 6-3. We want to have a length of four or magnitude of form. So first thing we want to do is convert it into a unit vector. So we find the magnitude of this and we see it going to be the square root of six birds. So 36 plus nine Class four, which is going to be seven. So now we get that are vector. Our unit vector Will be won over seven times this right here, if you want, you could always multiply that through. But then we're going to want to multiply this by four. So that way it's no longer a unit factor, but a factor with lengths four. So we see this would be 24/7, 12/7. 8/7. Mhm. Mhm. That's right. Here is going to be our final sector.

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