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Please help! - Vector Algebra - JEE Main-2

The value of a, for which the points A,B,C with position  vectors 2\hat{i}-\hat{j}+\hat{k},\; \; \hat{i}-3\hat{j}-5\hat{k}\; \; and\; \; a\hat{i}-3\hat{j}+\hat{k}  respectively are the vertices of a right angled triangle at c are

  • Option 1)

    2 and 1

  • Option 2)

    –2 and –1

  • Option 3)

    –2 and 1

  • Option 4)

    2 and –1

 
Answers (1)
95 Views
G gaurav

As we have learned

Scalar Product of two vectors -

\vec{a}.\vec{b}> 0 \:an\: acute\: angle

\vec{a}.\vec{b}< 0 \:an\: obtuse\: angle

\vec{a}.\vec{b}= 0 \:a\:right\: angle

- wherein

\Theta  is the angle between the vectors \vec{a}\:and\:\vec{b}

 

 

Position Vector -

If \vec{a} and \vec{b} are the position of vectors of two points A and B then

 \overrightarrow{AB}= \vec{b}-\vec{a}

\overrightarrow{AB}= P \vee of B - P\vee of A          

 

- wherein

 

 

\vec{AC}\cdot \vec{BC} = 0

\Rightarrow ((a\hat{i}-3\hat{j}+\hat{k})-(2\hat{i}-\hat{j}+\hat{k}))\cdot ((a\hat{i}-3\hat{j}+\hat{k})- (\hat{i}-3\hat{j}-5\hat{k}))=0

( a-2 )( a-1 )= 0 

a = 1,2 

 

 

 


Option 1)

2 and 1

Option 2)

–2 and –1

Option 3)

–2 and 1

Option 4)

2 and –1

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