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The figure shows a line $ L_1 $ in space and a second line $ L_2 $, which is the projection of $ L_1 $ onto the $ xy $-plane. (In other words, the points on $ L_2 $ are directly beneath, or above, the points on $ L_1 $.)(a) Find the coordinates of the point $ P $ on the line $ L_1 $.(b) Locate on the diagram the points $ A $, $ B $, and $ C $, where the line $ L_1 $ intersects the $ xy $-plane, the $ yz $-plane, and the $ xz $-plane, respectively.

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(a) $(2,1,4)$(b) $N=L_{2} \cap O y$$B \in L_{1}$ such that $N B \perp x y$ -plane

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Missouri State University

Campbell University

Baylor 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.

04:17

The figure shows a line $L…

01:30

01:07

02:59

Consider the point; (1, 3,…

11:00

Let $ L_1 $ be the line th…

03:06

Let $L_{1}$ be the line th…

02:20

Let $P(x, y, z)$ be a poin…

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