The vectors \vec{a}\; and \; \vec{b} are not perpendicular and \vec{c}\; and \; \vec{d} are two vectors satisfying : \vec{b}\; \times \; \vec{c}=\vec{b}\; \times \; \vec{d}and \vec{a}\cdot \vec{d}=0. Then the vector \vec{d} is equal to

  • Option 1)

    \vec{b}+\left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}

  • Option 2)

    \vec{c}-\left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}

  • Option 3)

    \vec{b}-\left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}

  • Option 4)

    \vec{c}+\left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}

 

Answers (1)

As we learnt in 

Vector Triple Product (VTP) -

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

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

- wherein

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

 

 \vec{b}\times \vec{d}\:=\:\vec{b}\times\vec{c}

(\vec{b}\times \vec{d})\times \vec{a}\:\:=(\vec{b}\times \vec{c})\times \vec{a}

(\vec{a}.\vec{b})\:\: \vec{d} - 0(\vec{b})=(\vec{a}.\vec{b})\vec{c}-(\vec{a}.\vec{c})\vec{b}

\\\vec{d}\:=\:\vec{c}-(\frac{\vec{a}.\vec{c}}{\vec{a}.\vec{b}})\vec{b}


Option 1)

\vec{b}+\left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}

This option is incorrect.

Option 2)

\vec{c}-\left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}

This option is correct.

Option 3)

\vec{b}-\left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}

This option is incorrect.

Option 4)

\vec{c}+\left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}

This option is 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..

₹ 4999/-
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