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  • I have a doubt, kindly clarify. - Let A be a point on the line and B(3,2,6) be a point in the space. Then the value of for which the - Three Dimensional Geometry - JEE Main

Let A be a point on the line \overrightarrow{r} = (1-3\mu )\widehat{i}+(\mu -1)\widehat{j}+(2+5\mu )\widehat{k} and B(3,2,6) be a point in the space. Then the value of \mu for which the vector \overrightarrow{AB} is parallel to the plane x-4y+3z = 1 is:

  • Option 1)

     

    1/4

  • Option 2)

     

    1/8

  • Option 3)

     

    1/2

  • Option 4)

     

    -1/4

Answers (1)

best_answer

 

Condition for line to be parallel to plane -

\vec{b}\cdot \vec{n}= 0 or a_{1}a+b_{1}b+c_{1}c= 0

-

Let point A on line be 

(1-3\mu )\hat{i}+(\mu -1)\hat{j}+(2+5\mu )\hat{k}  and  B(3,2,6) is point in space.

Then from the concept learnt,

\vec{AB}=(2+3\mu )\hat{i}+(3-\mu )\hat{j}+(4-5\mu )\hat{k}

which is parallel to the plane x-4y+3z=1

\therefore 2+3\mu -12+4\mu +12-5\mu =0

\mu =\frac{1}{4}


Option 1)

 

1/4

Option 2)

 

1/8

Option 3)

 

1/2

Option 4)

 

-1/4

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