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\vec a , \vec b , \vec c  are three vectors , then \vec a \times ( \vec b \times \vec c )-(\vec a \times \vec b) \times \vec c  equals 

Option: 1

\vec 0


Option: 2

 (\vec c \cdot \vec b) \vec a + ( \vec a \cdot \vec b) \vec c 


Option: 3

 (\vec a \cdot \vec b ) \vec c - (\vec c \cdot \vec b ) \vec a(\vec a \times \vec b) \times \vec c


Option: 4

(\vec c \cdot \vec b ) \vec a - (\vec a \cdot \vec b ) \vec c


Answers (1)

best_answer

As we have learned

Vector Triple Product (VTP) -

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

- wherein

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

 

 \vec a \times (\vec b \times \vec c) = (\vec a \cdot \vec c) \vec b - (\vec a \cdot \vec b ) \vec c

(\vec a \times \vec b) \times \vec c = (\vec c \cdot \vec a ) \vec b - (\vec c \cdot \vec b ) \vec a

\vec a \times ( \vec b \times \vec c)- (\vec a \times \vec b) \times \vec c = (\vec c \cdot \vec b ) \vec a - (\vec a \cdot \vec b ) \vec c

 

Posted by

Gaurav

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