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Given planes P1:cy+bz=x P2:az+cx=y P...

Given planes `P_1:cy+bz=x`
`P_2:az+cx=y`
`P_3:bx+ay=z`
`P_1, P_2 and P_3` pass through one line, if

A

`a^2+b^2+c^2=ab+bc+ca`

B

`a^2+b^2+c^2+2abc=1`

C

`a^2+b^2+c^2=1`

D

`a^2+b^2+c^2+2ab+2bc+2ca+2abc=1`

Text Solution

Verified by Experts

The correct Answer is:
(c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
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  2. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

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  3. Given planes P1:cy+bz=x P2:az+cx=y P3:bx+ay=z P1, P2 and P3 pass...

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  4. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  5. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z...

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  6. The line which contains all points (x, y, z) which are of the form (x,...

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  7. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

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  8. The equation of the plane which passes through the line of intersectio...

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  9. A straight line is given by r=(1+t)i+3tj+(1-t)k, where tinR. If this l...

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  10. The distance of the point (-1, -5, -10) from the point of intersection...

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  11. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

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  12. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  13. The orthogonal projection A' of the point A with position vector (1, 2...

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  14. The equation of the line passing through (1, 1, 1) and perpendicular t...

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  15. A variable plane at a distance of 1 unit from the origin cuts the axes...

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  16. The angle between the lines AB and CD, where A(0, 0, 0), B(1, 1, 1), C...

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  17. The shortest distance of a point (1, 2, -3) from a plane making interc...

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  18. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  19. The direction ratios of the line I1 passing through P(1, 3, 4) and per...

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