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Find the distance from the point to the given plane.

$ (1, -2, 4) , 3x + 2y + 6z = 5 $

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Distance $=\frac{18}{7}$

02:22

Wen Zheng

01:05

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Campbell University

University of Michigan - Ann Arbor

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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we have a question and this we need to find the distance of the plane. The X. Let's do I Plus six. That equal to five From a .1 Common -2 comma four. Okay so we have a formula for this if point is excellent. Common violin Commons that one. And plane is A X plus B. Y plus C. Said plus day. Then distance will be equal to excellent plus B. Y. One plus sees that one Bless D. Mud by a square must be a squared plus B squared the route. No. In our question that distance will be called to Excellent. First of all that is tragedies. Yeah plus two I plus six dead minus five equals to zero. So now let's split in. Excellent. Why won't comment that one? As here in this equation in this formula So three into 1 bless two and 2 -2 plastics into four minus five, divide by and models of course A193 square to square Plus six square under the scheduled So mark this is 3 -4 Plus 24 -5, divide by nine. Platform plus 36. So this is 24 plus 3, -9. That is 18 martin, divide by 36-plus 4. 40 49 in the root so 18 is always positive. So more mode can be removed. Models can be removed 18 by square root of 49 is seven. So distances 18 x seven units. Thank you

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