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Consider a pyramid OPQRS located in the ...

Consider a pyramid OPQRS located in the first octant `(xge0, yge0, zge0)` with O as origin and OP and OR along the X-axis and the Y-axis , respectively. The base OPQRS of the pyramid is a square with OP=3. The point S is directly above the mid point T of diagonal OQ such that TS=3. Then,

A

the acute angle between OQ and OS is `(pi)/(3)`

B

the equation of the plane containing ht `triangleOQS` is x-y=0

C

the length of perpendicular from P to the plane containing the `triangleOQS` is `(2)/(sqrt(3))`

D

the perpendicular distance from O to the straight line containing RS is `sqrt((15)/(2))`

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The correct Answer is:
`(b,c, d)`
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0...

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  2. Let P be the image of the point (3,1,7) with respect to the plane x-...

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  3. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

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  4. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

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  5. A line l passing through the origin is perpendicular to the lines l1...

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  6. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

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  7. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (x+1)/(5)=(y+1)/...

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  8. If the distance between the plane Ax-2y+z=d. and the plane containing ...

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  9. Read the following passage and answer the questions. Consider the line...

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  10. Read the following passage and answer the questions. Consider the line...

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  11. Consider the line L1 : (x +1)/3 = (y+ 2)/1= (z +1)/2 L2 : (x-2)/1=...

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  12. Consider three planes P1 : x-y + z = 1, P2 : x + y-z=-1 and P3 : x-...

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  13. Consider the planes 3x-6y-2z=15 and 2x+y-2z=5. find the angle between...

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  14. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  15. The distance of the point (1, 3, -7) from the plane passing through th...

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

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  17. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  18. The disatance of the point (1, 0, 2) from the point of intersection of...

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  19. The equation of the plane containing the line 2x-5y""+""z""=""3;""x...

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  20. The angle between the lines whose direction cosines satisfy the equa...

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