Q21 of 112 Page 1121

Find the vector equation of a line passing through the point having the position vector and parallel to the line joining the points with position vectors and Also, find the Cartesian equivalents of this equation.

Given: line passes through the point with position vector and parallel to the line joining the points with position vectors and .


To find: equation of line in vector and Cartesian forms


Formula Used: Equation of a line is


Vector form:


Cartesian form:


where is a point on the line and with b1 : b2 : b3 being the direction ratios of the line.


Explanation:


Here,


The direction ratios of the line are (1 - 2) : (-1 - 3) : (5 + 4)


⇒ -1 : -4 : 9


⇒ 1 : 4 : -9


So,


Therefore,


Vector form:



Cartesian form:



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