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Statement-I The point A(3, 1, 6) is the ...

Statement-I 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-II The plane `x-y+z=5` bisect the line segment joining `A(3, 1, 6) and B(1,3, 4)`.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
B
The coordinates of the mid point of AB are (2,2,5). Clearly it lies on `x-y+z=5`. So, statement -2 is true.
Direction ratios of AB are proportional to 2,-2,2 or 1,-1,1 which are proportional to the direction ratios of normal to the plane.
So,`A(3,1,6)` is the mirror image of `B(1,3,4)`. Hence statement -1 is true. But, statement -2 is not a correct explanation for statement -1.
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Assertion: The point A(3,1,6) is the mirror image of the point B(1,3,4) in the plane x-y+z=5. Reason: The plane x-y+z=5 bisects the line segment joining A(3,1,6) and B(1,3,4) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section II - Assertion Reason Type
  1. Consider the planes 3x-6y-2z=15 and 2x+y-2z=5. Statement 1:The parame...

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  2. Consider three planes P(1):x-y+z=1, P(2):x+y-z=-1 and P(3):x-3y+3z=2...

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  3. Statement 1: Let A,B,C be the image of point P(a,b,c) in YZ,ZX andXY p...

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  4. Consider the plane pi:x+y-2z=3 and two points P(2,1,6) and Q(6,5,-2). ...

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  5. Statement 1: Lthe cartesian equation of the plane vecr=(hati-hatj)+lam...

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  6. Statement 1: If the vectors veca and vecc are non collinear, then the ...

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  7. Statement 1: If a is an integer the the straight lines vecr=hati+2ha...

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  8. Statement-I The lines (x-1)/(1)=(y)/(-1)=(z+1)/(1) and (x-2)/(1)=(y+1)...

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  9. Statement 1: A point on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance...

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  10. Consider the line L:vecr(hati+3hatj-hatk)+lamda(hatj+2hatk) and the pl...

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  11. Statement 1: The plane 5x+2z-8=0 contains the line 2x-y+z-3=0 and 3x+y...

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  12. Statement-I The point A(3, 1, 6) is the mirror image of the point B(1,...

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  13. Statement-I The point A(1, 0, 7) is the mirror image of the point B(1,...

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  14. The equations of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3) a...

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  15. Given two straight lines whose equations are (x-3)/1=(y-5)/(-2)=(z-7...

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  16. Statement 1: The shortest distance between the lines x/2=y/(-1)=z/2 an...

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