Home
Class 12
MATHS
Find the distance of a point (2,5,-3) fr...

Find the distance of a point (2,5,-3) from the plane . `vec(r) (6 hat(i) - 3 hat(j) + 2 hat(k))` = 4

Text Solution

Verified by Experts

The correct Answer is:
` d = (13)/(7)` units
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic - 3 (Long answer type questions - II)|23 Videos

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic - 3 (Short answer type questions - I)|3 Videos

  • SOLVED PAPER ( Topper Answers March - 2015 )

    OSWAAL PUBLICATION|Exercise PART - E|4 Videos

  • VECTOR ALGEBRA

    OSWAAL PUBLICATION|Exercise Topic - 4 (Short Answer Type Questions - II|7 Videos

Similar Questions

Explore conceptually related problems

Find the distance of the point (2,3,-5) from the plane vec(r)* (hat(i) + 2 hat(j) - 2 hat(k))= 9 .

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes vec(r) * (hat(i) - hat(j) + 2 hat(k)) = 5 and vec(r)* (3 hat(i) + hat(j) + hat(k)) = 6

Find the coordinates of the foot of the bot and the length of the bot drawn from the point P(5,4,2) to the line. vec(r) = - hat(i) + 3 hat(j) + hat(k) + lambda (2 hat(i) + 3 hat(j) - hat(k)) . Also find the image of P in this line.

Write the vector equation of the plane passing through the point (a,b,c) and parallel to the plane vec(r) *(hat(i)=hat(j)+hat(k)) = 2

Find the distance of the point (2,12,5) from the point of intersection of the lines vec(r) = (2 hat(i) - 4 hat(j) + 2 hat(k)) + lambda (3 hat(i) + 4 hat(j) + 2 hat(k)) and the plane r * (hat(i) - 2 hat(j) + hat(k)) = 0

Find the image of the point having position vector (hat(i) + 3 hat(j) + 4 hat(k)) in the plane vec(r)* (2 hat(i) - hat(j) + hat(k)) + 3 = 0

Find the equation of the plane passing through the point P(1,1,1) and containing the line vec(r) = (-3 hat(i) + hat(j) + 5 hat(k)) + lambda (3 hat(i) - hat(j) - 5 hat(k)) . Also, show that the plane contains the line vec(r) = (- hat(i) + 2 hat(j) + 5hat(k)) + mu (hat(i) - 2 hat(j) - 5 hat(k)) .

Find the vector equation of the plane passing through three points with position vectors (hat(i) + hat(j) - 2 hat(k)),(2 hat(i) - hat(j) + hat(k)) and (hat(i) + 2 hat(j) + hat(k)) . Also find the coordinates of the point of intersection of this plane and the line vec(r) = (3 hat(i) - hat(j) - hat(k)) + lambda (2 hat(i) - 2 hat(j) + hat(k)) .

Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )

Find the value of lambda if the vectors vec(a) = 3hat(i) + hat(j) - 2hat(k) and vec(b) = hat(i) + lambda hat(j) - 3hat(k) are perpendicular to each other.

Home
Profile