By Jazar R.N.

ISBN-10: 0470398353

ISBN-13: 9780470398357

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**Sample text**

247) The circle is made when the parameter θ varies by 2π. The arc length between θ = 0 and θ = π/2 would then be one-fourth the perimeter of the circle. 251) where f (x, y, z) = 0 and g(x, y, z) = 0 represent two surfaces. The space curve would then be indicated by intersecting the surfaces. 252) where a and k are constant and ϕ is an angular variable. 260) Example 47 Two Points Indicate a Line Consider two points A and B with position vectors a and b in a coordinate frame. The condition for a point P with position vector r to lie on the line AB is that r − a and b − a be parallel.

Axis. A straight line that indicates the line on which the vector is. The vector axis is also called the line of action. 3. End point. A start or an end point indicates the point at which the vector is applied. Such a point is called the affecting point. 4. Direction. The direction indicates at what direction on the axis the vector is pointing. 5. Physical quantity. Any vector represents a physical quantity. If a physical quantity can be represented by a vector, it is called a vectorial physical quantity.

3 Fundamentals of Kinematics Vector Deﬁnition By a vector we mean any physical quantity that can be represented by a directed section of a line with a start point, such as O, and an end point, such as P. We may show a −→ − → vector by an ordered pair of points with an arrow, such as OP . The sign PP indicates a zero vector at point P. Length and direction are necessary to have a vector; however, a vector may have ﬁve characteristics: 1. Length. The length of section OP corresponds to the magnitude of the physical quantity that the vector is representing.

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