PQRS is a parallelogram. If  and , then what is  equal to ?

This question was previously asked in
NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)
View all NDA Papers >

Answer (Detailed Solution Below)

Option 4 :
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

Concept:

The diagonals of the parallelogram bisect each other.

In a triangle PQR,  ​ 

For any vector 

Calculation:

Given:   and 

Let the diagonals of the parallelogram intersect each other at O.

⇒   __(1)

(∵ The diagonals of the parallelogram bisect each other.)

As,   and 

⇒   and , __(2)

From (1) and (2),

⇒   __(3)

Now in triangle PQO,

 +  +  = 0

⇒ 

⇒ 

Putting the values from equation (3),

⇒ 

⇒  = 

∴ The correct option. is (4) .

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 star apk mpl teen patti teen patti joy official teen patti master apk download