Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let \alpha \epsilon R and the three vectors

\vec{a}=\alpha\hat{i}+\hat{j}+3\hat{k} , \vec{a}=2\hat{i}+\hat{j}-\alpha \hat{k} and 

\vec{a}=\alpha \hat{i}-2\hat{j}+3 \hat{k} . Then the set 

S=\left \{{\alpha: \vec{a},\vec{b}\: \: and \: \: \vec{c}\: \: are\: \: coplanar }}{ \right \}

  • Option 1)

    is singleton

  • Option 2)

    is empty

  • Option 3)

    contains exactly two positive numbers

  • Option 4)

    contains exactly two numbers only one of which is positive

 

Answers (1)

\begin{vmatrix} \alpha & 1 & 3\\ 2 & 1 & -4\\ \alpha & -2 &-3 \end{vmatrix}=0

=>  3\alpha ^{2}+18=0

=>  \alpha \epsilon \phi


Option 1)

is singleton

Option 2)

is empty

Option 3)

contains exactly two positive numbers

Option 4)

contains exactly two numbers only one of which is positive

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Result 2024 Live: JEE Mains session 2 results at jeemain.nta.ac.in soon; rank predictor
anam-khan

JEE Main 2024 session 2 final answer key out at jeemain.nta.ac.in; steps to check probable scores
anam-khan

JEE Main Result 2024 Live: Download session 2 final answer key at jeemain.nta.ac.in; rank predictor, cutoff

Latest Question