Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • I have a doubt, kindly clarify. - Vector Algebra - JEE Main-2

If \vec{u},\vec{v}\; and\; \vec{w} are three non-­coplanar vectors, then (\vec{u}+\vec{v}-\vec{w})\cdot (\vec{u}-\vec{v})\times (\vec{v}-\vec{w})  equals

  • Option 1)

    \vec{u}\cdot \vec{v}\times \vec{w}

  • Option 2)

    \vec{u}\cdot \vec{w}\times\vec{v}

  • Option 3)

    3u\cdot \vec{u}\times\vec{w}

  • Option 4)

    0

 

Answers (1)

best_answer

As we learnt in 

Scalar Triple Product -

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

=\left (\vec{a}\times \vec{b}\right)\cdot \vec{c}= \vec{a}\cdot \left ( \vec{b} \times \vec{c}\right )

=\left (\vec{b}\times \vec{c}\right)\cdot \vec{a}= \vec{b}\cdot \left ( \vec{c} \times \vec{a}\right )

=\left (\vec{c}\times \vec{a}\right)\cdot \vec{b}= \vec{c}\cdot \left ( \vec{a} \times \vec{b}\right )

- wherein

Scalar Triple Product of three vectors \hat{a},\hat{b},\hat{c}.

 

 

 

(\vec{u}+\vec{v}-\vec{w})\cdot (\vec{u}-\vec{v})\times (\vec{v}-\vec{w})

\Rightarrow\begin{bmatrix} \vec{u} + \vec {v}- \vec {w}\right ] & \vec{u} -\vec {v} & \vec{v} - \vec {w} \end{bmatrix}

\Rightarrow \begin{vmatrix} 1 & 1& -1 \\ 1 & -1 & 0 \\ 0 & 1 & -1 \end{vmatrix} \left [ \vec {u} \ \vec{v}\ \vec{w}\right ]

=\left [ \vec {u} \ \vec{v} \ \vec{w}\right ]

= \vec {u}. (\vec{v} \times \vec{w})

 


Option 1)

\vec{u}\cdot \vec{v}\times \vec{w}

This option is correct.

Option 2)

\vec{u}\cdot \vec{w}\times\vec{v}

This option is incorrect.

Option 3)

3u\cdot \vec{u}\times\vec{w}

This option is incorrect.

Option 4)

0

This option is incorrect.

Posted by

prateek

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 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question