Directions : Question are Assertion- Reason type questions. Each of these questions contains two statements. Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices,only one of which is the correct answer. You have to select the correct choice:

Statement-1 : The point A (3, 1, 6) is the mirror image of the point B (1, 3, 4) in the plane x-y+z=5.

Statement-2 : The plane x-y+z=5 bisects the line segment joining A (3, 1, 6) and B (1, 3, 4).

  • Option 1)

    Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.

  • Option 2)

    Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.

  • Option 3)

    Statement -1 is true, statement -2 is false.

  • Option 4)

    Statement -1 is false, statement -2 is true.

 

Answers (1)

As we learnt in 

Image of a point -

Let L' be the image of point P\left ( \alpha ,\beta ,\gamma \right ) in the plane ax+by+cz+d=0

L' will be given by the formula 

\frac{x-\alpha }{a}=\frac{y-\beta }{b}=\frac{z-\gamma }{c}= \frac{-2\left ( a\alpha +b\beta +c\gamma +d \right )}{a^{2}+b^{2}+c^{2}}

-

 \frac{x-1}{1}=\frac{y-3}{-1}=\frac{z-4}{1}= \frac{-2(-3)}{3}

x= 3, y=1, z=6

Statement 1 is true as well.

But it is not necessary that if a plane bisects line joining A and B, that B is the image of A.

 


Option 1)

Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.

Incorrect option

Option 2)

Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.

Correct option

Option 3)

Statement -1 is true, statement -2 is false.

Incorrect option

Option 4)

Statement -1 is false, statement -2 is true.

Incorrect option

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