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The line which contains all points `(x, y, z)` which are of the form `(x, y, z)=(2, -2, 5)+lambda(1, -3, 2)` intersects the plane `2x-3y+4z=163` at P and intersects the YZ-plane at Q. If the distance PQ is `asqrt(b)`, where `a,binN and agt3`, then `(a+b)` is equalto

A

23

B

95

C

27

D

None of these

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The correct Answer is:
A
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DISHA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Exercise -2 : Concept Applicator
  1. The equation of the line intersection of the planes 4x+4y-5z=12 and 8x...

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  2. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

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

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  4. Show that the points A(1,2,3), B(-1,-2,-1), C(2,3,2), D(4,7,6) are the...

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  5. The shortest distance between the line 1+x=2y=-12z and x=y+2=6z-6 is

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  6. The line which passes through the origin and intersect the two lines (...

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  7. The angle between the lines (x+1)/2 = (y+3)/2 = (z-4)/-1 and (x-4)/1 =...

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  8. The distance between the line given by vecr= hati+hatj + lamda(hati-2...

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  9. Find the point on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance of 3s...

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  10. The coordinates o the foot of the perpendicular drawn from the orig...

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  11. If A,B,C are point (1,0,4) , (0,-1,5) and (2,-3,1) respectively , then...

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  12. If from a point P(a ,b ,c) prpendiculars P Aa n dP B are drawn to y za...

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  13. The equation of the plane which makes with coordinate axes a triangle ...

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  14. The plane ax+by=0 is rotated through an angle alpha about its line of ...

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  15. The plane x + 3y + 13 = 0 passes through the line of intersection of t...

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  16. A variable plane at distance of 1 unit from the origin cuts the coordi...

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  17. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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

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  19. If the distance between the plane Ax 2y + z = d and the plane contain...

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

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