If the position vector of a point P with respect to origin O is î + 3ĵ - 2k̂ and that of a point Q is 3î + ĵ - 2k̂, then what is the position vector of the bisector of the angle POQ? 

  1. î - ĵ - k̂ 
  2. î + ĵ - k̂ 
  3. î + ĵ + k̂ 
  4. None of the above

Answer (Detailed Solution Below)

Option 4 : None of the above
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
5.8 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Concept:

 A triangle ABC is said to be an isosceles triangle if triangle ABC must have two sides of equal length.

Calculations:

Given, the position vector of a point P with respect to origin O is î + 3ĵ - 2k̂ and that of a point Q is 3î + ĵ - 2k̂.

\(\rm \bar {OP} \) = î + 3ĵ - 2k̂ and  \(\rm \bar {OQ}\) = 3î + ĵ - 2k̂.

⇒ |OP| = \(\rm \sqrt {1+9 + 4} = \sqrt {14}\)

⇒ |OQ| = \(\rm \sqrt {9 + 1+ 4} = \sqrt {14}\)

Here, |OP| = |OQ|

\(\rm \triangle POQ\) is isoscale.

The position vector of the bisector of the angle POQ = \(\rm \dfrac 1 2 (OP + OQ)\)

⇒The position vector of the bisector of the angle POQ = \(\rm \dfrac 1 2 [(î + 3ĵ - 2k̂) + (3î + ĵ - 2k̂)]\)

⇒The position vector of the bisector of the angle POQ = \(\rm \dfrac 1 2 (4î + 4ĵ - 4k̂) \)

⇒The position vector of the bisector of the angle POQ = \(\rm 2î + 2ĵ - 2k̂\)

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had 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. 

More Applications of Vectors Questions

More Vector Algebra Questions

Get Free Access Now
Hot Links: teen patti cash teen patti online game teen patti list dhani teen patti