Q. 215.0( 1 Vote )

# 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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