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  • Find x such that the four points A(4,4,4),B(5,x,8),C(5,4,1) and D(7,7,2) are coplanar.         <div style="float:left;

Find x such that the four points A(4,4,4),B(5,x,8),C(5,4,1) and D(7,7,2) are coplanar.

 

 

 

 
 
 
 
 

Answers (1)

Let
\therefore \vec{a}= \overrightarrow{OB}-\overrightarrow{OA}= \hat{i}+\left ( x-4 \right )\hat{j}+4\hat{k}
    \vec{b}= \overrightarrow{OC}-\overrightarrow{OA}= \hat{i}+0\hat{j}-3\hat{k}
  \vec{c}= \overrightarrow{OD}-\overrightarrow{OA}= 3\hat{i}+3\hat{j}-2\hat{k}
As the points are coplaner so \left [ \vec{a}, \vec{b}, \vec{c} \right ]= \begin{vmatrix} 1 & x-4 &4 \\ 1& 0 &-3 \\ 3& 3 & -2 \end{vmatrix}= 0
\Rightarrow 1\left ( 0+9 \right )-\left ( x-4 \right )\left ( -2+9 \right )+4\left ( 3-0 \right )= 0
                                                                                          \therefore x= 7  

Posted by

Ravindra Pindel

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