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In a tetrahedron OABC, if OA=hat(i), OB=...

In a tetrahedron OABC, if `OA=hat(i), OB=hat(i)+hat(j) and OC=hat(i)+2hat(j)+hat(k)`,if shortest distance between egdes OA and BC is m, then `sqrt(2)m` is equal to …(where O is the origin).

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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Integer Answer Type Questions)
  1. In a tetrahedron OABC, if OA=hat(i), OB=hat(i)+hat(j) and OC=hat(i)+2h...

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  2. A parallelopiped is formed by planes drawn through the points (2, 3, 5...

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  3. If the perpendicular distance of the point (6 5, 8) from the y-axis is...

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  4. If the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/...

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  5. If the planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a line, ...

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  6. If xz-plane divide the join of point (2, 3, 4) and (1, -1, 5) in the r...

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  7. If the triangle ABC whose vertices are A(-1, 1, 1), B(1, -1, 1) and C(...

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  8. The equation of a plane which bisects the line joining (1, 5, 7) and (...

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  9. The shortest distance between origin and a point on the space curve ...

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  10. Show that the plane2x-2y+a+12=0 touches the sphere x^(2)+y^(2)+z^(2)-2...

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  11. If the centroid of tetrahedron OABC where A,B,C are given by (a,2,3),(...

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  12. If the circumcentre of the triangle whose vertices are (3, 2, -5), (-...

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  13. If overline(P1P2) is perpendicular to overline(P2P3), then the value o...

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  14. Let the equation of the plane containing line x-y-z-4=0=x+y+2z-4 and...

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  15. Let P(a, b, c) be any on the plane 3x+2y+z=7, then find the least valu...

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  16. The plane denoted by P1 : 4x+7y+4z+81=0 is rotated through a right ang...

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  17. The distance of the point P(-2, 3, -4) from the line (x+2)/(3)=(2y+3)/...

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  18. The position vectors of the four angular points of a tetrahedron OABC ...

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  19. Value of lambda do the planes x-y+z+1=0, lambdax+3y+2z-3=0, 3x+lambday...

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  20. If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least...

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