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Find $ a + b , 4a + 2b , \mid a \mid $, and $ \mid a - b \mid $.

$ a = 4i - 3j + 2k , b = 2i - 4k $

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01:34

Alan Ghazarians

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Campbell University

University of Michigan - Ann Arbor

Idaho State 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.

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Yeah. For the given problem, we want to evaluate some of the functions knowing that A. Is going to be vector for negative 32 Mhm. And B will be the victor two negative four or 20 negative for so some of these factors A plus B is going to be four plus 26 maybe a three plus zero standing free. And then to minus four is going to be negative too. So that the sum of the vectors in the components. Now let's look at how to calculate the magnitude. It's gonna be very similar to how it was before the square root of fourth grade, which is 16 Plastic Square root of negative surplus. A negative free spread which is nine. Um so it's gonna be 25 And then 25-plus 4. So we'll have route 29 as the magnitude.

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