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The line which contains all points (x, y...

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

(a)`23`

B

(b)`95`

C

(c)`27`

D

(d)None of these

Text Solution

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The correct Answer is:
(a)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  2. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, 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. If the position vectors of the points A,B and C be hati+hatj,hati-hatj...

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  5. Find the equation of plane passing through the line of intersection o...

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

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  7. Find the distance of the point (-1, -5, -10) from the point of interse...

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  8. What is the Next Prime Number after 7 ?

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

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

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

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  12. Find the value of x Equation is x+7=4

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

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

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  15. A tetrahedron has vertices of O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C...

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

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  17. Equation of the plane through three points A, B and C with position ve...

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  18. OABC is a tetrahedron. The position vectors of A, B and C are i, i+j a...

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  19. The plane x-y-z=4 is rotated through an angle 90^(@) about its line of...

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  20. A(xy),A(yz),A(zx) be the area of projections of an area on the xy,yz a...

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