Consider the following statements in respect of a vector , where :

1.  is perpendicular to 

2.  is perpendicular to 

Which of the above statement is/are correct?

This question was previously asked in
NDA (Held On: 18 Apr 2021) Maths Previous Year paper
View all NDA Papers >
  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 3 : Both 1 and 2
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

CONCEPT:

  • The scalar triple product of three vectors is zero if any two of them are equal
  • If  is perpendicular to the vectors  then 

CALCULATION:

Given:  , where 

Statement 1 is perpendicular to 

First let's find out 

⇒ 

As we know that, 

⇒ 

∵ It is given that 

⇒ 

⇒ 

Hence, statement 1 is true.

Statement 2 is perpendicular to 

First let's find out 

⇒ 

As we know that, the scalar triple product of three vectors is zero if any two of them are equal

⇒ 

Hence, statement 2 is true.

Hence, the correct option is 3.

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. 

More Scalar Triple Product Questions

More Vector Algebra Questions

Hot Links: teen patti yas teen patti casino all teen patti game