Answer :

__Given:__ line passes through (-1, 3, -2) and is perpendicular to each of the lines and

__To find:__ equation of line in Vector and Cartesian form

__Formula Used:__ Equation of a line is

Vector form:

Cartesian form:

where is a point on the line and is a vector parallel to the line.

If 2 lines of direction ratios a_{1}:a_{2}:a_{3} and b_{1}:b_{2}:b_{3} are perpendicular, then a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3} = 0

__Explanation:__

Here,

Let the direction ratios of the line be b_{1}:b_{2}:b_{3}

Direction ratios of the other two lines are 1 : 2 : 3 and -3 : 2 : 5

Since the other two line are perpendicular to the given line, we have

b_{1} + 2b_{2} + 3b_{3} = 0

-3b_{1} + 2b_{2} + 5b_{3} = 0

Solving,

Therefore,

Vector form of the line is:

Cartesian form of the line is:

Rate this question :

Find the equationMathematics - Board Papers

Find the vector aMathematics - Board Papers

Write the vector Mathematics - Board Papers

Find the value ofMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers