端木·宇 2008-6-19 20:35
What's a Vector
A [b]vector[/b] is a mathematical object possessing, and fully described by, a [b]magnitude[/b] and a [b]direction[/b].It’s possible to talk about vectors simply in terms of numbers, butit’s often a lot easier to represent them graphically as arrows. Thevector’s magnitude is equal to the length of the arrow, and itsdirection corresponds to where the arrow is pointing. Physicistscommonly refer to the point of a vector as its [b]tip[/b] and the base as its [b]tail[/b].
[align=center][img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/29a4b00cf26ff3d3cbbf3f4c57161034.gif[/img][/align]
There are a number of ways to label vectors. You may have seen vectors labeled [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/3f6281f96e80fc18e33f56d633172726.gif[/img] or [i]A[/i].This book will follow the convention you’ll find on SAT II Physics:vectors are written in boldface and vector magnitudes in plain script.For example, vector [i][b]A[/b][/i] has magnitude [i]A[/i].
[b] Vectors vs. Scalars[/b]
In contrast to a vector quantity, a [b]scalar[/b]quantity does not have a direction; it is fully described by just amagnitude. Examples of scalar quantities include the number of words inthis sentence and the mass of the Hubble Space Telescope. Vectorquantities you’ll likely come across quite frequently in physicsinclude displacement, [i][b]s[/b][/i]; velocity, [i][b]v[/b][/i]; acceleration, [i][b]a[/b][/i]; force, [i][b]F[/b][/i]; momentum, [i][b]p[/b][/i]; electric field, [i][b]E[/b][/i]; and magnetic field, [i][b]B[/b][/i].
When in doubt, ask yourself if a certainquantity comes with a direction. If it does, it’s a vector. If itdoesn’t, it’s a scalar.
[b] Example[/b]
Which of the following sentences deal with vector quantities?
I. “I used to drive a 10-ton truck.”
II. “You’ll find a gas station if you follow this road 20 miles due north.”
III. “The 10-volt battery is the one on your left.”
(A)I only
(B)II only
(C)III only
(D)II and III
(E)I, II, and III
“I used to drive a 10-ton truck” deals withmass, which is a scalar quantity. When we know that a truck weighs 10tons, we don’t need to ask, “in what direction?” “You’ll find a gasstation if you follow this road 20 miles due north” deals with thevector quantity of displacement. When asking directions to a gasstation, you don’t simply want to know how far it is from where youare, but also in what direction you need to go. “The 10-volt battery isthe one on your left” is slightly tricky: volts are a scalarquantity—you don’t ask in what direction the battery’s volts are going.However, you might be deceived by the mention of “on your left.”However, “on your left” is a reference to the battery, not to thevolts. The magnitude “10 volts” doesn’t have a direction, so thatquantity is a scalar. The answer is [b]B[/b].
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