Q. 10

Find the equations of the line passing through the point (-1, 3, -2) and perpendicular to each of the lines and

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 a1:a2:a3 and b1:b2:b3 are perpendicular, then a1b1+a2b2+a3b3 = 0


Explanation:


Here,


Let the direction ratios of the line be b1:b2:b3


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


b1 + 2b2 + 3b3 = 0


-3b1 + 2b2 + 5b3 = 0


Solving,






Therefore,


Vector form of the line is:



Cartesian form of the line is:



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Revision of straight lines important formulas in one shot59 mins
Concept Builder Questions of straight Lines (Quiz Session)55 mins
Magnetic field due to current carrying straight wireFREE Class
Translation Process37 mins
Interactive Quiz on Bacterial Diseases29 mins
Immune System Disorders60 mins
Human health & diseases (Drug)56 mins
Get to know all about Immune SystemFREE Class
Interactive Quiz on Cancer36 mins
Interactive Quiz on Magnetic field due to straight wire & circular loopFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses