Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

If a · b =0 and a × b = 0 then which one of the following is...

If a⃗⋅b⃗=0\vec{a} \cdot \vec{b}=0 and a⃗×b⃗=0→\vec{a} \times \vec{b}=\overrightarrow{0} then which one of the following is correct?

Options

  1. Aa⃗\vec{a} is parallel to b⃗\vec{b}
  2. Ba⃗\vec{a} is perpendicular to b⃗\vec{b}
  3. Ca⃗=0\vec{a}=0 or b⃗=0→\vec{b}=\overrightarrow{0}
  4. DNone of the above

Correct answer

C. a⃗=0\vec{a}=0 or b⃗=0→\vec{b}=\overrightarrow{0}

Step-by-step solution

The correct answer is option C.
Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

Passage: Let a × b = c and b × c = a . Question: Consider the following statements : I. (… NDA 2026Passage: Let a , b , c , a + b , b + c , a + b + c be unit vectors. Question: What is the… NDA 2026Passage: Let a , b , c be unit vectors. Further, a is perpendicular to b ; c makes an… NDA 2026Passage: Let a , b , c , a + b , b + c , a + b + c be unit vectors. Question: What is the… NDA 2026Passage: Let a × b = c and b × c = a . Question: Consider the following statements : I. a… NDA 2026Passage: Let a , b , c be unit vectors. Further, a is perpendicular to b ; c makes an… NDA 2026What is the area of the parallelogram whose sides are represented by the vectors i + 2 j… NDA 2025Let p = a - b , q = a + b . If | a | = | b | = 2 and a · b = 2 , then what is the value… NDA 2025A force F = 2 i - λ j + 5 k is applied at the point A(1, 2, 5) . If its moment about the… NDA 2025ABC is a triangle right-angled at B . If A(k, 1, -1) , B(2k, 0, 2) and C(2+2k, k, 1) are… NDA 2025Consider the following statements in respect of a vector d = ( a × b ) × c : I. d is… NDA 2025The position vectors of three points A , B and C are a , b and c respectively such that 3… NDA 2025The position vectors of three points A , B and C are a , b and c respectively, where c =… NDA 2025Let a , b , ( a × b ) be unit vectors. What is ( a · b ) equal to? NDA 2025Let θ be the angle between two unit vectors a and b . If a +2 b is perpendicular to 5 a… NDA 2024What is 3 α+2 β equal to if (2 i +6 j +27 k ) ×( i +α j +β k ) is a null vector? NDA 2024 Full Vector Algebra list Vector Algebra JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs