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Find $ a + b , 4a + 2b , \mid a \mid $, and $ \mid a - b \mid $.
$ a = \langle 8, 1, -4 \rangle , b = \langle 5, -2, 1 \rangle $
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01:53
Alan Ghazarians
Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 2
Vectors
Knowledge S.
February 2, 2021
Is it me going nuts or does 9+9+25=45? Sgould not it equal 43?
Johns Hopkins University
Oregon State University
Harvey Mudd College
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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for the given problem, we want to evaluate to some of the factors knowing that vector A is going to be 8 1 -4 And the B vector is going to be 5 -2, 1 with some of these vectors. If we do A plus B, okay, is going to be the component added together. So eight plus 5 13, 1 minus two, negative one and negative four plus one negative three. Then we want to find the magnitude of a. So magnitude of A is going to be the square root of eight squared, which is 64 Plus one Squared, which is one Um plus a negative 4th grade, which is 16. That takes us to 81 squared of 81 we know is nine. So that's the magnitude and this is the final answer.
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