मूल बिंदु से समतल x + y + z = 3 पर खींचे गए लंब का पाद ______ है।

This question was previously asked in
NDA (Held On: 18 Apr 2021) Maths Previous Year paper
View all NDA Papers >
  1. (0, 1, 2)
  2. (0, 0, 3)
  3. (1, 1, 1)
  4. (-1, 1, 3)

Answer (Detailed Solution Below)

Option 3 : (1, 1, 1)
Free
NDA 01/2025: English Subject Test
5.3 K Users
30 Questions 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

अवधारणा:

एक बिंदु P (x1, y1, z1) से समतल ax + by + cz + d = 0 की लंब दूरी निम्न द्वारा दी जाती है: \(d = \left| {\frac{{a{x_1} + b{y_1} + c{z_1} + d}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}} \right|\)

गणना :

माना A(x, y, z) मूल बिंदु से समतल x + y + z = 3 पर खींचे गए लंब का पाद है।

जैसा कि हम जानते हैं कि एक बिंदु P (x1, y1, z1) से समतल ax + by + cz + d = 0 की लंब दूरी निम्न द्वारा दी जाती है: \(d = \left| {\frac{{a{x_1} + b{y_1} + c{z_1} + d}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}} \right|\)

तो, मूल और समतल x + y + z - 3 = 0 के बीच की दूरी निम्न द्वारा दी गई है: \(d = \left| {\frac{{0 + 0 + 0 - 3}}{{\sqrt {{1^2} + {1^2} + {1^2}} }}} \right| = \frac{3}{\sqrt 3} = \sqrt 3\)
तो, इसका मतलब है कि मूल बिंदु को मिलाने वाली रेखा की लंबाई और A, 3 है
जैसा कि हम देख सकते हैं कि दिए गए विकल्पों में से, यदि A = (1, 1, 1) है, तो मूल बिंदु और A के बीच की दूरी √3 है।
अत: सही विकल्प 3 है।
Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Distance from a Plane Questions

More Three Dimensional Geometry Questions

Get Free Access Now
Hot Links: teen patti master gold apk teen patti rummy teen patti master purana