Q. 285.0( 2 Votes )

# Find the distance

Answer : Let the point be A = (-2, 3, -4)

The line is Compare line with Where is point on the line and is the direction of line and The point on line is (1, 2, -1) and direction is <1, 3, -9>

Rewriting the line equation in cartesian from Let it be equal to k so that we can write the general point on the line x – 1 = k and y – 2 = 3k and z + 1 = -9k

x = k + 1 and y = 3k + 2 and z = -9k – 1

So, any general point on the line say B has coordinates (k + 1, 3k + 2, -9k – 1)

We have to measure the distance from point A to the line parallel to the plane x – y + 2z – 3 = 0

Comparing x – y + 2z – 3 = 0 with general plane equation ax + by + cz + d = 0 where <a, b, c> is the normal to the plane

let the normal is Say we have to find the distance AB such that AB is parallel to plane

AB parallel to plane which means AB is perpendicular to the normal of plane that is CD  As is perpendicular to their dot product is zero because the right hand side will have cos90° which is 0  k + 3 + (3k – 1) (-1) + (-9k + 3)2 = 0

k + 3 – 3k + 1 – 18k + 6 = 0

-20k + 10 = 0

20k = 10

k = 1/2

Putting k = 1/2 in B we will get the point B

B = (1/2 + 1, 3(1/2) + 2, -9(1/2) – 1) Now the distance AB   Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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 RELATED QUESTIONS :

Find the equationMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the distanceMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the CartesiaMathematics - Board Papers

Find the coordinaMathematics - Board Papers