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Introduction to vectors. A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
We defined a vector in Rn as an n-tuple, i.e., as an n×1 matrix. This is an algebraic definition of a vector where a vector is just a list of num-bers. The geometric objects we will look at in this chapter should be seen as geometric interpretations of this alge-braic definition.
Depictions of geometric angles will look like the one shown in this figure: s 1 s 2 V Figure 1.1.1 The above figure depicts a non-flat geometric angle \s 1s 2, with vertex V. The flat angles are: the straight angles, whose sides are opposite “halves” of a line; the trivial angles, whose sides coincide. Any non-flat angle \s 1s
Vectors in R3. Introduce a coordinate system in 3-dimensional space in the usual way. First choose a point O called the origin, then choose three mutually perpendicular lines through O, called the x, y, and z axes, and establish. a number scale on each axis with zero at the origin.
Three numbers are needed to represent the magnitude and direction of a vector quantity in a three dimensional space. These quantities are called vector quantities. Vector quantities also satisfy two distinct operations, vector addition and multiplication of a vector by a scalar.
1 Define Sine, Cosine and Tangent in terms of the opposite, adjacent and hypotenuse of a triangle. 2 Use the above trig functions to finds angles and right triangle side lengths. 3 Define a vector in a sentence.
A triangle has vertices at A(− −2, 2,0), B(6,8,6) and C(−6,8,12). Find the area of the triangle ABC. 90
