The length of the perpendicular drawn from the point (2,1,4) to the plane 

containing the lines \vec{r}=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})  and 

\vec{r}=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k}) is : 

 

  • Option 1)

    3

  • Option 2)

    \frac{1}{3}

  • Option 3)

    \sqrt{3}

  • Option 4)

    \frac{1}{\sqrt{3}}

 

Answers (1)

Perpendicula vector to the plane

\vec{w}= \begin{vmatrix} \hat{i} & \hat{j} &\hat{k} \\ 1& 2 &-1 \\ -1&1 &-2 \end{vmatrix}=-3\hat{i}+3\hat{j}+3\hat{k}

Equation of the plane 

-3(x-1)+3(y-1)+3z=0

Equation => x-y-z=0

d_{(2,1,4)}=\frac{|2-1-4|}{\sqrt{1^{2}+1^{2}+1^{2}}}=\sqrt3

 


Option 1)

3

Option 2)

\frac{1}{3}

Option 3)

\sqrt{3}

Option 4)

\frac{1}{\sqrt{3}}

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