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If $ a = \langle 3, 0, -1 \rangle $ find a vector $ b $ such that $ comp_a b = 2 $.

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$\langle 0,0,-2 \sqrt{10}\rangle$ or any vector of the form $\langle s, t, 3 s-2 \sqrt{10}\rangle, s, t \in \mathbb{R}$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

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.

02:59

If $a=\langle 3,0,-1\rangl…

04:27

If a = 2, 0, −1 , find a v…

02:39

If $\mathbf{a}=[3,0,-1],$ …

01:31

If $x=\langle 3,0,-1\rangl…

01:34

If $\mathbf{a}=\langle 3,0…

01:20

02:31

Compute with these vectors…

04:31

Let $A=\left[\begin{array}…

The problem is, if a is equal to 3 negative 1 point find a vector b such that the scattered projection of b unto a is equal to 2 point. So blot b is equal to e 123 point, then, by the definition of the scale projection of b. Unto a we have a dot b over magnitude of a is equal to 2 point. So behalf 3 b, 1 minus b 3 over root of 10 is equal to 2, so 3 b, 1 minus b 3 is equal to 2 times root of 10 point. We can choose b, 1, equal to 0 v, 3 equal to negative 2 times. The root of 10 and b 2 can be. Any number can not be 2 equal to 1. We worked here, 01 negative 2 times 0 to 10 point. So if, if b, is equal to this work here, then the scaler projection of b a is equal to 2.

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