# Find the Cartesian and vector equations of the line passing through the point (1, 2, -4) and perpendicular to each of the lines and Given: line passes through (1, 2, -4) 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 other two lines are 8 : -16 : 7 and 3 : 8 : -5

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

8b1 – 16b2 + 7b3 = 0

3b1 + 8b2 – 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 wire37 mins  Translation Process37 mins  Interactive Quiz on Bacterial Diseases29 mins  Immune System Disorders60 mins  Interactive Quiz on Cancer36 mins  Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins  Interactive Quiz on Connective & Epithelial Tissue45 mins  Human health & diseases (Drug)56 mins
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 