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If the angle between the line `x=(y-1)/(2)=(z-3)(lambda)` and the plane `x+2y+3z=4 is cos^(-1)(sqrt((5)/(14)))`, then `lambda` equals

A

`(3)/(2)`

B

`(2)/(5)`

C

`(5)/(3)`

D

`(2)/(3)`

Text Solution

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The correct Answer is:
(d)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. An equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit...

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

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

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

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

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

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  7. A line AB in three-dimensional space makes angles 45^(@) and 120^(@) w...

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

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  9. Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) lies in the plane x+3y-alp...

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  10. The projection of a vector on the three coordinate axes are 6, -3, 2, ...

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  11. The line passing through the points (5, 1, a) and (3, b, 1) crosses th...

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  12. If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3...

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  13. Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=...

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  14. If a line makes an angle (pi)/(4) with the positive directions of each...

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  15. If (2, 3, 5) is one end of a diameter of the sphere x^(2)+y^(2)+z^(2)-...

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  16. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular ...

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  17. The image of the point (-1, 3, 4) in the plane x-2y=0 is

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  18. If the plane 2ax-3ay+4az+6=0 passes through the mid point of the line ...

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

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  20. The angle between the lines 2x=3y=-z and 6x=-y=-4z is

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