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Differentiation of Scalar and Vector Quantity

Scalar Vector

Quantities that are fully described by a magnitude

(or numerical value) alone.

For example, the units for time (minutes, days,

hours,etc.) represent an amount of time only and

tell nothing of direction. Additional examples

ofscalar quantities are density, mass, and energy.

Quantities that are fully described by both a

magnitude and a direction.

Any physical quantity that has both magnitude

(size) and direction, such as velocity, acceleration,

or force,

Represented either geometrically by an arrow

whose length corresponds to its magnitude and

points in an appropriate direction, or by two or

three numbers representing the magnitude of its

components.

Polygon method:

Two vectors A and B are added by drawing the arrows which represent the vectors in such a way that

the initial point of B is on the terminal point of A. The resultant C = A + B, is the vector from the initialpoint of A to the terminal point of B.

Many vectors can be added together in this way by drawing the successive vectors in a head-to-tail

fashion, as shown here on the left.

If the polygon is closed, the resultant is a vector of zero magnitude and has no direction. This is called

the NULL VECTOR, or 0.

Parallelogram method:

In the parallelogram method for vector addition, the vectors are translated, (i.e., moved) to a commonorigin and the parallelogram constructed as follows:

The resultant R is the diagonal of the parallelogram drawn from the common origin.

Pythagorean Theorem

It is the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the

length of the hypotenuse.

In simpler terms the Pythagorean Theorem is a formula that is used when trying to find a missing side in

a right triangle.

The formula is a^2 + b^2 = c^2

C in the Pythagorean Theorem is always the hypotenuse.

Review; the hypotenuse is the side opposite of the right angle in a right triangle.

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A and B in the Pythagorean Theorem are the two remaining sides. No specific side for either variable.

Cosine Law

Intrigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths

of the sides of a planetriangleto thecosineof one of itsangles.

Law of Cosines Formula

Sine Law

Intrigonometry, the law of sines (also known as the sine law, sine formula, orsine rule) is

anequationrelating thelengthsof the sides of an arbitrarytriangleto thesinesof its angles.

The Law of Sines (or Sine Rule) is very useful for solving triangles:

It works for any triangle:

a, b and c are sides.

A, B and C are angles.

(Side a faces angle A,

side b faces angle B and

side c faces angle C).

http://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Cosinehttp://en.wikipedia.org/wiki/Cosinehttp://en.wikipedia.org/wiki/Cosinehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Lengthshttp://en.wikipedia.org/wiki/Lengthshttp://en.wikipedia.org/wiki/Lengthshttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Sinehttp://en.wikipedia.org/wiki/Sinehttp://en.wikipedia.org/wiki/Sinehttp://en.wikipedia.org/wiki/Sinehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Lengthshttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Cosinehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trigonometry