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The three vectors hat i+hat j,hat j+hat ...

The three vectors `hat i+hat j,hat j+hat k, hat k+hat i` taken two at a time form three planes, The three unit vectors drawn perpendicular to these planes form a parallelopiped of volume:

A

`(1)/(3)`

B

`4`

C

`3(sqrt(3))/(4)`

D

`(4)/(3sqrt(3))`

Text Solution

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The correct Answer is:
(d)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The distance of the point (-1, -5, -10) from the point of intersection...

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  2. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

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

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

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

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  6. A variable plane at a distance of 1 unit from the origin cuts the axes...

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

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

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  9. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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

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

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

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

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  14. A(xy),(yz),A(zx) be the area of projections oif asn area a o the xy,yz...

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  15. Through a point P(h,k,l) a plane is drawn at righat angle to OP to mee...

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  16. The volume of the tetrahedron included between the plane 3x+4y-5z-60=0...

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  17. The angle between the lines whose direction cosines are given by the ...

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  18. The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-...

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  19. The cartesian equations of the plane perpendicular to the line (x-1)/(...

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  20. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

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