Chapter 3 vectors

What is a vector?
A vector is a quantity with both a size—its magnitude—and a direction. Vectors you’ll meet in the next few chapters include position, displacement, velocity, acceleration, force, and momentum.
>> LOOKING BACK Tactics Box 1.1 on vector addition

How are vectors added and subtracted?
Vectors are added "tip to tail." The order of addition does not matter. To subtract vectors, turn the subtraction into addition by writing →A−→B=→A+(−→B).A→−B→=A→+(−B→). The vector −→B−B→ is the same length as →BB→ but points in the opposite direction.

What are unit vectors?
Unit vectors define what we mean by the +x−+x− and +y−directions+y−directions in space.

• A unit vector has magnitude 1.

• A unit vector has no units.

Unit vectors simply point.

What are components?
Components of vectors are the pieces of vectors parallel to the coordinate axes—in the directions of the unit vectors. We write →E=Exˆι=EyˆJE→=Exι^=EyJ^ Components simplify vector math.

How are components used?
Components let us do vector math with algebra, which is easier and more precise than adding and subtracting vectors using geometry and trigonometry. Multiplying a vector by a number simply multiplies all of the vector’s components by that number. →C=2→A+3→BC→=2A→+3B→ means {Cx=2Ax+3BxCy=2Ay+3By{Cx=2Ax+3BxCy=2Ay+3By

How will I use vectors?
Vectors appear everywhere in physics and engineering—from velocities to electric fields and from forces to fluid flows. The tools and techniques you learn in this chapter will be used throughout your studies and your professional career.