Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2007Paper 1
Exam
JEE Advanced
Year
2007
Paper
Paper 1
Subject
Mathematics
Chapter
Vector Algebra

JEE Advanced 2007 · Paper 1 · Mathematics · Vector Algebra

The number of distinct real values of λ , for which the vectors...

The number of distinct real values of λ\lambda, for which the vectors −λ2i^+j^+k^-\lambda^2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, i^−λ2j^+k^\hat{\mathbf{i}}-\lambda^2 \hat{\mathbf{j}}+\hat{\mathbf{k}} and i^+j^−λ2k^\hat{\mathbf{i}}+\hat{\mathbf{j}}-\lambda^2 \hat{\mathbf{k}} are coplanar, is

Options

  1. Azero
  2. Bone
  3. Ctwo
  4. Dthree

Correct answer

C. two

Step-by-step solution

∣−λ2111−λ2111−λ2∣=0⇒λ6−3λ2−2=0⇒(1+λ2)2(λ2−2)=0⇒λ=±2\begin{aligned}& \left|\begin{array}{ccc} -\lambda^2 & 1 & 1 \\ 1 & -\lambda^2 & 1 \\ 1 & 1 & -\lambda^2 \end{array}\right|=0 \Rightarrow \lambda^6-3 \lambda^2-2=0 \\ & \Rightarrow \quad \left(1+\lambda^2\right)^2 \left(\lambda^2-2\right)=0 \Rightarrow \lambda=\pm \sqrt{2}\\ & \end{aligned}
Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

Let a , b be two vectors, and let P, Q and R be the points with position vectors a , b… JEE Advanced 2026Let a = 4 i - j + 3 k , b = 10 i + 2 j - k and a vector c be such that 2( a × b ) + 3( b… JEE Main 2026Let a = 2 i + 3 j + 3 k and b = 6 i + 3 j + 3 k . Then the square of the area of the… JEE Main 2026If a = i + j + k , b = j - k and c be three vectors such that a × c = b and a · c = 3… JEE Main 2026Let O be the origin, OP = a and OQ = b . If R is the point on OP such that OP = 5 OR… JEE Main 2026Let a = 7 i + j - k and b = j + 2 k . If r is a vector such that r × a + a × b = 0 and r… JEE Main 2026Let u and v be unit vectors inclined at an acute angle such that | u × v |= 3 2 . If A =λ… JEE Main 2026Let a_k = ( θ_k) i + j and b_k = i - ( θ_k) j , where θ_k = 2^ k-1 π 2^n + 1 , for some n… JEE Main 2026Let the vectors a = - i + j + 3 k and b = i + 3 j + k . For some λ, μ ∈ ℝ , let c = λ a +… JEE Main 2026Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j . If… JEE Main 2026If a and b are two vectors such that | a | = 2 and | b | = 3 , then the maximum value of… JEE Main 2026Let P be a point in the plane of the vectors A B =3 i + j - k and A C = i - j +3 k such… JEE Main 2026For three unit vectors a , b , c satisfying | a - b |^ 2 +| b - c |^ 2 +| c - a |^ 2 =9… JEE Main 2026Let P Q R be a triangle such that P Q =-2 i - j +2 k and PR =a i +b j -4 k , a, b ∈ ℤ .… JEE Main 2026Let a =2 i -5 j +5 k and b = i - j +3 k . If c is a vector such that 2( a × c )+3( b × c… JEE Main 2026Let a =2 i - j - k , b = i +3 j - k and c =2 i + j +3 k . Let v be the vector in the… JEE Main 2026 Full Vector Algebra list Vector Algebra JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs