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OABC is a tetrahedron. The position vect...

OABC is a tetrahedron. The position vectors of A, B and C are `I, i+j and j+k`, respectively. O is origin. The height of the tetrahedron (taking ABC as base) is

A

`(1)/(2)`

B

`(1)/(sqrt(2))`

C

`(1)/(2sqrt(2))`

D

None of these

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The correct Answer is:
(b)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The direction ratios of the line I1 passing through P(1, 3, 4) and per...

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

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

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

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

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

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

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

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

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

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

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  12. A plane makes interceptsOA, OB and OC whose measurements are a, b and ...

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  13. The radius of the circle in which the sphere x^2+y^2+z^2+2x-2y-4z-19=0...

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  14. Let veca=hati+ hatj and vecb = 2hati-hatk . The point of intersection ...

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  15. The co-ordinate of the point P on the line r=(hat(i)+hat(j)+hat(k))+la...

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  16. The 3-dimensional vectors v1, v2, v3 satisfying v1cdotv1=4, v1cdotv2=-...

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  17. The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equi...

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  18. A, B, C and D are four points in space. Using vector methods, prove th...

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  19. Show that x(1) hati+y(1) hatj+ z1hatk, x2hati+y2hatj+z2hatk and x3hati...

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  20. The position vectors of points of intersection of three planes rcdotn1...

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