Explanation Consider a line that passes through a point with position vector r 0 and it is parallel to a vector v . The vector equation for a line is written as follows. r = r 0 + t v Here, r 0 is the position vector, t is the scalar parameter, and v is the vector which is parallel to the line. Thus, the vector equation for a line is r = r 0 + t v _ . To write: The parametric equations for a line. Solution: The parametric equations for a line are x = x 0 + a t , y = y 0 + b t , z = z 0 + c t _ . Consider a line that passes through a point P ( x 0 , y 0 , z 0 ) and it is parallel to a direction vector v = 〈 a , b , c 〉 . The parametric equations for a line are written as follows. x = x 0 + a t , y = y 0 + b t , z = z 0 + c t Here, ( x 0 , y 0 , z 0 ) is a point through which the line passes and a , b , and c are the direction numbers of direction vector v

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ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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A vector equation for a line.

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