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If angle theta between the line (x+1)/1=...

If angle `theta` between the line `(x+1)/1=(y-1)/2=(z-2)/2` and the plane `2x-y+sqrt(lambda)z+4=0` is such that `sin theta=1//3,` the value of `lambda` is
a. `-3/5`
b. `5/3`
c. `-4/3`
d. `3/4`

A

`-(4)/(3)`

B

`(3)/(4)`

C

`(5)/(3)`

D

`-(3)/(5)`

Text Solution

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The correct Answer is:
C
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ICSE-THREE DIMENSIONAL GEOMETRY-MULTIPLE CHOICE QUESTIONS
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  2. If the planes x+2y+kz=5 and 2x +y-2z=0 are at right angles, then the v...

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  3. The ratio in which the line segment joining the points (-2,4,5) and (3...

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  4. The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to ...

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  5. distance between the parallel planes ax+by+ cz + d =0 and ax+by + cz +...

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  6. Equations of the line passing through (1,1,1) and perpendicular to th...

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

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  8. If a variable plane moves so that the sum of the reciprocals of its in...

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

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

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  11. A vector parallel to the line of intersection of the planes overset(to...

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  12. The locus represented by xy+yz=0 is

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  13. If the planes overset(to)( r) (2 hat(i) - lambda (j) + 3 hat(k) ) = 0 ...

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  14. The equation of the plane passing through the point (1, 1, 0) and perp...

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  15. The distance of the point (2,1,-1) from the plane x-2y + 4z =9 is

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  16. The angle between a line with direction ratios lt 2, 2, 1gt and a line...

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  17. The lines (x-x1)/(a) = (y-y1)/(b) = (z-z1)/( c ) and (x-x1)/(a') = (y-...

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  18. The vector equation of the line passing through the points A(3,4,-7) a...

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  19. The vector equation of the line passing through the point (-1,5,4) and...

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  20. The line (x-2)/(3) = (y-3)/(4)= (z-4)/(5) is parallel to the plane

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