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If the vectors \underset{AB}{\rightarrow} = 3\hat{i}+4\hat{k}  and    \underset{AC}{\rightarrow}  = 5\hat{i}-2\hat{j}+4\hat{k}  are the sides of a triangle ABC ,then the length of the median through A is :

  • Option 1)

    \sqrt{45}

  • Option 2)

    \sqrt{18}

  • Option 3)

    \sqrt{72}

  • Option 4)

    \sqrt{33}

 

Answers (1)

As learnt in concept

Mid point formula -

\frac{\vec{a}+\vec{b}}{2}

- wherein

If \vec{a} and \vec{b} , position vector of mid-point of AB

 \frac{\overrightarrow {AB}+\overrightarrow{AC}}{2}=\overrightarrow{AD}

\overrightarrow {AD}=4\vec{i}+\vec{j}+4\vec{k}

\left | \overrightarrow {AD} \right |=\sqrt{4^{2}+1^{2}+4^{2}}=\sqrt{33} 


Option 1)

\sqrt{45}

This option is incorrect 

Option 2)

\sqrt{18}

This option is incorrect 

Option 3)

\sqrt{72}

This option is incorrect 

Option 4)

\sqrt{33}

This option is correct 

Posted by

Sabhrant Ambastha

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