-Vectors show up everywhere in physics.
-Some physical quantities that are represented as vectors are: displacement, velocity, acceleration, force, momentum, and electric and magnetic fields.
-For now, we will study two-dimensional vectors (flat plane)
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DEFINITION
Vector- a quantity that involves both magnitude and direction and obeys the commutative law of addition.
Scalar- a quantity that does not involve in direction.
EX: 55 miles per hr is scalar, while 55 miles per hr, to the north is a vector
Other examples of scalars: mass, power, temperature, and electric charge
Vectors can be denoted in several ways:
A, A, or an A with an arrow on top
the two on the left are for textbooks while the one on the right is used in handwritten documents
Displacement (net distance traveled plus direction) is the prototypical example of a vector:
A= 4 miles to the north
displacement magnitude direction
B= 3 miles to the east
displacement magnitude direction
When we say that vectors obey the commutative law for addition, we mean that if we have two vectors of the same type, then A+B must equal B+A. The vector sum A+B means the vector A followed by B, while the vector sum B+A means the vector B followed by A.
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VECTOR ADDITION (GEOMETRIC)
Vectors are drawn as arrows. The tail is where the vector originates and the tip is where the arrow is. The sum of two vectors is expressed in a "tip-to-tail" method. (as seen in the above picture)
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SCALAR MULTIPLICATION
A vector can be multiplied by a scalar (a #), and the result is a vector. If the original vector is A and the scalar is k, then the scalar multiple kA is as follows:
magnitude of kA= |k| x (magnitude of A)
direction of kA= the same as A if k is positive OR the opposite of A if k is negative
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VECTOR SUBTRACTION (GEOMETRIC)
To subtract one vector form another, for example, to get A-B, simply form the vector -B, which is the scalar multiple (-1)B, and add it to A:
A - B = A + (-B)
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