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

Consider three planes `P_(1):x-y+z=1`
`P_(2):x+y-z=-1`
and `" "P_(3):x-3y+3z=2`
Let `L_(1),L_(2),L_(3)` be the lines of intersection of the planes `P_(2)` and `P_(3),P_(3)` and `P_(1),P_(1)` and `P_(2)` respectively.
Statement I Atleast two of the lines `L_(1),L_(2)` and `L_(3)` are non-parallel.
Statement II The three planes do not have a common point.

A

Statement-I is true, Statement II is also true, Statement-II is the correct explanation of Statement-I.

B

Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement -II is true.

Text Solution

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The correct Answer is:
(d)
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Consider three planes p _(1): x-y+z=1, p _(1)P: x + y-z=-1 and p _(3) :x - 3y+ 3z =2. Let I_(1), I _(2), I _(3) the lines of intersection of the planes P _(2)and P _(3) , P _(3) and P _(1), P _(1) and P _(2), respectively. Statement I : Atleast two of the lines I_(1), I_(2) are non-parallel. Statement II : The three planes do not have a common point. For the following question, choose the correct answer from the codes (A), (B), (C ) and (D) defined as follows.

Consider the planes p _(1) : 2x + y+ z+4=0 p _(2) :y -z+4 =0 and p _(3) : 3x+ 2y +z+8=0 Let L_(1),I _(2), I_(3) be the lines of intersection of the planes P_(2)and P_(3), P_(3) and P _(1),P_(1) and P _(2) respectively. Then:

Consider three planes P_1 : x-y + z = 1, P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3, P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point

Consider three planes P_1:x-y+z=1, P_2:x+y-z=-1,P_3,x-3y+3z=2 Let L_1,L_2,L_3 be the lines of intersection of the planes P_2 and P_3 and P-1,P_1 and P_2, respectively.

Let P_(1) and P_(2) be two planes containing the lines L_(2) and L_(2) respectively. STATEMENT-1 : If P_(1) and P_(2) are parallel then L_(1) and L_(2) must be parallel. and STATEMENT-2 : If P_(1) and P_(2) are parallel the L_(1) and L_(2) may not have a common point.

Let P_(1) : 2x + y + z + 1 = 0 P_(2) : 2x - y + z + 3 = 0 and P_(3) : 2x + 3y + z + 5 = 0 be three planes, then the distance of the line of intersection of planes P_(1) = 0 and P_(2) = 0 from the plane P_(3) = 0 is

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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Read the following passage and answer the questions. Consider the line...

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

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  4. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

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  5. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  6. The distance of the point (1, 3, -7) from the plane passing through th...

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  7. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  8. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  9. The disatance of the point (1, 0, 2) from the point of intersection of...

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  10. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  11. The angle between the lines whose direction cosines satisfy the equ...

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  12. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+...

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  13. Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is

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  14. If the lines (x-2)/1=(y-3)/1)(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 ar...

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  15. An equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit...

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  16. If the line (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/...

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  17. If the angle between the line x=(y-1)/(2)=(z-3)(lambda) and the plane ...

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

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  19. The length of the perpendicular drawn from the point (3, -1, 11) to th...

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  20. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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