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Let $ C $ be the point on the line segment $ AB $ that is twice as far from $ B $ as it is from $ A $. If $ a = \vec{OA}, b = \vec{OB}, $ and $ c = \vec{OC} $, that $ c = \frac{2}{3} a + \frac{1}{3} b $.

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"Show thatc $=2 / 3 \mathrm{a}+1 / 3 \mathrm{b} .$ "- Proven in work.

02:16

Wen Zheng

04:19

Bobby Barnes

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Johns Hopkins University

Harvey Mudd College

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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Let $ C $ be the point on …

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Find the midpoint of the …

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Given points $A, B,$ and $…

and and it is given there to see is the point online segment A B. That is twice as far be from. Okay. So if this is a line segment A B and C. Is the point. Okay, C. Is the point? Um that is twice as far be as it is from. Mm. So if this is C. Okay, And if this is X, this becomes two x. And given that small is oh, a vector small, B. S O. B victor, and C. Is the victor? Okay. Uh huh. Okay. If this is oh so a vector is a then we will be victorious. B. Okay. And we'll see victories. See selected, going to show that sequel to two or three A plus one by three. B. Yeah. Okay, so if this is like this, so a B victor If A B. S. X. So this is one by three, this is okay. And see victor be returned evicted this, you see. So here, if we write it as a C. Like this, so in the strangle we can write a vector equal to sorry, evicted place X. Vector or vector will be equal to see victor. Similarly here we can right see vector plus expect so I do expect equal to ah be evicted. If we could just eliminate the value of facts, we have to multiply this with two. So this becomes to a vector Plus two Expected equal to to see Victor and see victor place to expect. It will be equal to be evicted. Now subtract minus minus minus this will get cancelled out. So we should right here as to a vector minus c vector equal to to see vector minus b victor. So if we add selected to both, the sides will be getting three C vector equal to be vector plus. Do it victor. So let's divide both sides by three will be getting see victory equal to two by three A vector place one x 3 B victor. This is being written here as a sequel to to buy three a Plus one x 3 B. Since Fruit. Thank you.

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