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The vectors  \overrightarrow{AB}=3\hat{i}+4\hat{k}\; \; and\; \;\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}  are the sides of a triangle ABC.  The length of the median through  A is 

  • Option 1)

    \sqrt{72}\;

  • Option 2)

    \; \sqrt{33}\;

  • Option 3)

    \; \sqrt{288}\;

  • Option 4)

    \; \sqrt{18}\; \;

 

Answers (1)

As we learnt in

Mid point formula -

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

- wherein

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

 Median is \frac{\overrightarrow {AB} + \overrightarrow {AC}}{2}

\\ = \frac {3\hat {i}+4\hat {k} + 5\hat{i}- 2 \hat {j} + 4 \hat{k}}{2} \\ = 4 \hat {i} - \hat{j} + 4 \hat{k}

Length of Mediam |\overrightarrow{AD}|= \sqrt{4^{2}+1^{2}+4^{2}} = \sqrt{33}


Option 1)

\sqrt{72}\;

This option is incorrect.

Option 2)

\; \sqrt{33}\;

This option is correct.

Option 3)

\; \sqrt{288}\;

This option is incorrect.

Option 4)

\; \sqrt{18}\; \;

This option is incorrect.

Posted by

Vakul

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