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If (\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}), where \vec{a},\vec{b}\; and\; \vec{c} are any three vectors such that \vec{a}\cdot \vec{b}\neq 0, \; \; \vec{b}\cdot \vec{c}\neq 0,  then \vec{a}\; \; and\; \; \vec{c} are

  • Option 1)

    inclined at an angle of  \pi /3  between them

  • Option 2)

    inclined at an angle of  \pi /6  between them

  • Option 3)

    perpendicular

  • Option 4)

    parallel

 

Answers (1)

best_answer

As we have learned

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.

 

 

Collinear Vectors -

Two vectors are said to be collinear if and only if there exists a scalar m such as that \vec{a}=m\vec{b}

- wherein

m is a Scalar.

 

 Vector triple product 

\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}

\Rightarrow ( \vec b \cdot \vec c )\vec a = (\vec a \cdot \vec b )\vec c

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

\Rightarrow \vec a = \lambda\vec c

collinear vectors \vec a \: \: and \: \: \vec c

 

 

 

 

 


Option 1)

inclined at an angle of  \pi /3  between them

Option 2)

inclined at an angle of  \pi /6  between them

Option 3)

perpendicular

Option 4)

parallel

Posted by

Himanshu

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