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  3. Using vectors, prove that the points (2,-1),(3,-5,1) and (-1,11,9) are collinear.        
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Using vectors, prove that the points (2,-1),(3,-5,1) and (-1,11,9) are collinear.

 

 

 

 
 
 
 
 

Answers (1)
R Ravindra Pindel

Let A(2,-1,3), B(3,-5,1) and C(-1,11,9)
Here \overrightarrow{AB}= \hat{i}-4\hat{j}-2\hat{k},\: \overrightarrow{AC}= -3\hat{i}+12\hat{j}+6\hat{k}
\because \overrightarrow{AC}= -3\overrightarrow{AB}\; \; \; \overrightarrow{AC}\parallel \overrightarrow{AB}
But A is a common point so, A,B and C are collinear.

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