English
Hindi

Question

Download Solution PDF

The length of the perpendicular drawn from the origin to the plane 2x - 3y + 6z - 42 = 0 is

  1. 3
  2. 4
  3. 5
  4. 6

Answer (Detailed Solution Below)

Option 4 : 6
Free Tests
View all Free tests >
Free
Agniveer Navy SSR Full Test - 01
100 Qs. 100 Marks 60 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

The distance of a point (p, q, r) from the plane ax + by + cz + d = 0

D = 

Calculation:

Given the equation of the plane is 

2x - 3y + 6z - 42 = 0

The distance of the plane from the origin (0, 0, 0)

D = 

D =  = 

D = 6

Download Solution PDF
Latest Indian Navy Agniveer SSR Updates

Last updated on Jun 20, 2025

-> The Indian Navy SSR Agniveeer Merit List has been released on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

Exams Tests Super Practice

More Distance from a Plane Questions

Q1.Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R in the plane P is:
Q2.Let a, b∈R. If the mirror image of the point P(a, 6, 9) with respect to the line (x – 3)/7 = (y – 2)/5 = (z – 1)/(-9) is (20, b, -a -9), then |a + b| is equal to:
Q3.The distance of the plane \(\rm \vec{r} \cdot\left(\frac{2}{7} \hat{i}+\frac{3}{7} \hat{j}-\frac{6}{7} \hat{k}\right)\) = 1 from the origin is
Q4.Figure-out the distance of a point (2, 5, -3) from the plane \(\vec{r}\). \((6\hat{i}-3\hat{j}+2\hat{k})\) = 6
Q5.Distance of the plane \(\overrightarrow {\rm{r}} \,{\rm{.}}\,\left( {{\rm{2\hat i}}\,{\rm{ - }}\,{\rm{\hat j}}\,{\rm{ + }}\,{\rm{2\hat k}}} \right)=12\), from the origin is ______.
Q6.If α and β are the lengths of the perpendiculars from the points (2, 3,-5) and (3,1,1) respectively from the plane x + 2y - 2z - 9 = 0, then α and β are the roots of the equation:
Q7.The distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 = 0 is
Q8.Find the possible value of k for which the distance between two plane 6x + 3y - 2z + k = 0 and 3x + 1.5y - z + 2 = 0 is 5 ?
Q9.Find the distance between the planes 2x + y - 2z + 6 = 0 and 4x + 2y - 4z - 6 = 0 ?
Q10.The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is

More Three Dimensional Geometry Questions

Q1.What is the point of intersection of L and P? 
Q2.What are the direction ratios of the line?  
Q3.If 〈l, m, n〉 are direction cosines of S, then what is the value. of 43 (I2 - m2 - n2)?  
Q4.Which of the following are the direction ratios of S? 
Q5.The centre of the sphere lies on the plane 
Q6.What is the diameter of the sphere? 
Q7.The distance of the point (1, 1, 9) from the point of intersection of the line (x – 3)/1 = (y – 4)/2 = (z – 5)/2 and the plane x + y + z = 17 is:
Q8.The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is:
Q9.Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R in the plane P is:
Q10.Let a, b∈R. If the mirror image of the point P(a, 6, 9) with respect to the line (x – 3)/7 = (y – 2)/5 = (z – 1)/(-9) is (20, b, -a -9), then |a + b| is equal to:

Indian Navy Agniveer SSR Important Links

Admit CardEligibility CriteriaResultSyllabus and Exam PatternCut OffBooks

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti game online teen patti 100 bonus teen patti joy vip