If  \vec{a},\vec{b},\vec{c} are non-­coplanar vectors and \lambda is a real number, then the vectors \vec{a}+2\vec{b}+3\vec{c},\; \lambda\vec{b}+4\vec{c}\; \; and\; \; (2\lambda -1)\vec{c} are non-­coplanar for

  • Option 1)

    all except two values of \lambda

  • Option 2)

    all except one values of \lambda

  • Option 3)

    all values of  \lambda

  • Option 4)

    no value of   \lambda

 

Answers (1)

As we learnt in 

Coplanar vectors -

\left [ \vec{a}\;\vec{b}\;\vec{c} \right ]=0

- wherein

\vec{a}\vec{b} and \vec{c} are three vectors.

 

 Condition for given three vectors to be

Coplanar is \begin{vmatrix} 1 & 2 &3 \\ 0& \lambda &4 \\ 0 & 0 & 2\lambda-1 \end{vmatrix}=0

\Rightarrow \lambda(2\lambda -1)=0

\Rightarrow \lambda =0, \lambda=\frac{1}{2}

They are non coplanar for all real \lambda except \lambda=0,\frac{1}{2}


Option 1)

all except two values of \lambda

Correct

Option 2)

all except one values of \lambda

Incorrect

Option 3)

all values of  \lambda

Incorrect

Option 4)

no value of   \lambda

Incorrect

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 6999/- ₹ 5/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions