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INTRODUCING VECTORS. 1.1 Scalars. 1.2 Vectors. 1.3 Unit vectors. 1.4 Vector algebra. 1.5 Simple examples. 1.1 Scalars. A scalar is a quantity with magnitude but no direction, any mathematical entity that can be represented by a number. Examples: Mass, temperature, energy, charge ...
Example. Write the polar unit vectors r and θ in terms of the Cartesian unit vectors x and y . Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction.
Overview. Many of you will know a good deal already about Vector Algebra — how to add and subtract vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors.
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.
Vector (or cross) product of two vectors, definition: a b = jajjbj sin ^n. where ^n is a unit vector in a direction. perpendicular. To get direction of a b use right hand rule: i) Make a set of directions with your right hand! thumb & first index finger, and with middle finger positioned perpendicular to plane of both.
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.
A vector of length 1 is called a unit vector. If ~v6=~0, then ~v=j~vjis a unit vector. EXAMPLE: If ~v= (3;4), then ~v= (2=5;3=5) is a unit vector, ~i;~j;~kare unit vectors.
