\vec{a},\vec{b},\vec{c}  are three vectors, such that \vec{a}+\vec{b}+\vec{c}=0,\; \; \left | \vec{b} \right |=2,\; \left | \vec{c} \right |=3,  then \vec{a}\cdot \vec{b}\; +\;\vec{b}\cdot \vec{c}\; +\vec{c}\cdot \vec{a}\;  is equal to

  • Option 1)

    –7

  • Option 2)

    7

  • Option 3)

    1

  • Option 4)

    0

 

Answers (1)

As we learnt in

Scalar Product of two vectors (dot product) -

\vec{a}\vec{b}=\left | a \right |\left | b \right |Cos\theta

- wherein

\Theta is the angle between the vectors\vec{a}\: and\:\vec{b}

 

 

\vec{a}+ \vec {b}+ \vec{c}=0

\left | \vec{a} \right |=1; \left | \vec{b} \right|=2; \left| \vec{c} \right |=3

(\vec{a}+ \vec {b}+ \vec{c})^{2}=0

\left | \vec{a} \right |^{2}+\left | \vec{b}\right |^{2} + \left| \vec{c} \right | ^{2} + 2 (\vec a. \vec{b}+\vec{b}.\vec{c}+\vec{a}.\vec{c}) =0

1+4 +9+ 2 (\vec a. \vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}) =0

2 (\vec a. \vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}) =-14

(\vec a. \vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}) =-7

 


Option 1)

–7

This option is correct.

Option 2)

7

This option is incorrect.

Option 3)

1

This option is incorrect.

Option 4)

0

This option is incorrect.

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