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What is the difference between vectors and scalars?
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A scalar is a quantity expressed by a single real number. An example of a scalar is length . A scalar has magnitude, or the size of a mathematical object. A vector is a quantity that is defined by multiple scalars. In addition to magnitude, a vector also has a direction.

For example if we are to find the magnitude of vector AB where the initial point A is (2, 2) and the end point B is (6, 4).

Substituting the values into our distance formula:

AB = √[(6-2)^2 + (4-2)^2 ]= √[4 2  + 2 2] = √[16 + 4] = √20

The magnitude/size of AB = 4.72 which is known as scalar as we do not know direction of AB yet.

To find the direction of a vector AB we measure the angle that the vector makes with a horizontal line using the formula:

tanx = (y2 – y1)/(x2 – x1)

= (2-4)/(2-6) = -2/-4

= 1/2

x = 26.57 degrees , finally direction of AB is 26.57 degrees and magnitude of sqrrot(20)
by Diamond (38,545 points)

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