Answer (Detailed Solution Below)

Option 1 :
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

Concept:

If θ is the angle between the line  and the plane a2 x + b2 y + c2 z + d = 0 then

Calculation:

Given: Equation of line is  and equation of plane is  3x + 4y + z + 5 = 0.

As we know that the angle between the line  and the plane a2 x + b2 y + c2 z + d = 0 is given by: 

Here, a1 = 3, b1 = - 1, c1 = 2, a2 = 3, b2 = 4 and c2 = 1.

⇒ a1 ⋅ a2 + b1 ⋅ b2 + c1 ⋅ c2 = 9 - 4 + 2 = 7

Latest NDA Updates

Last updated on Jun 18, 2025

->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.

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

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

-> 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. 

Hot Links: teen patti wealth teen patti master gold download teen patti flush teen patti sequence