Home
Class 12
MATHS
Find the value of lambda so that the poi...

Find the value of `lambda` so that the points `P ,Q ,R` and `S` on the sides `O A ,O B ,OC` and `A B ,` respectively, of a regular tetrahedron `O A B C` are coplanar. It is given that `(O P)/(O A)=1/3,(O Q)/(O B)=1/2,(O R)/(O C)=1/3` and `(O S)/(A B)=lambdadot` (A) `lambda=1/2` (B) `lambda=-1` (C) `lambda=0` (D) for no value of `lambda`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

O is the circumcenter of A B Ca n dR_1, R_2, R_3 are respectively, the radii of the circumcircles of the triangle O B C ,O C A and OAB. Prove that a/(R_1)+b/(R_2)+c/(R_3) =(a b c)/(R_3)

O P Q R is a square and M ,N are the midpoints of the sides P Q and Q R , respectively. If the ratio of the area of the square to that of triangle O M N is lambda:6, then lambda/4 is equal to 2 (b) 4 (c) 2 (d) 16

A,B,C are three points on the axes of x, y and z respectively at distance a, b,c from the origin O, find the co-ordinate of the point which is equidistant from A, B, C and O

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is 4:1 (b) 2:1 (c) 8:3 (d) 7:3

If R is a relation from a set A to t B and S is a relation form B to a set C then the relation S o R

A variable line through the point P(2,1) meets the axes at a an d b . Find the locus of the centroid of triangle O A B (where O is the origin).

A triangle A B C is inscribed in a circle with centre at O , The lines A O ,B Oa n dC O meet the opposite sides at D , E ,a n dF , respectively. Prove that 1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle

Let O be the origin, and O X x O Y , O Z be three unit vectors in the direction of the sides Q R , R P , P Q , respectively of a triangle PQR. If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P) is: -3/2 (b) 5/3 (c) 3/2 (d) -5/3

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio : (A) 1:2 (B) 3:2 (C) 2:1 D) 4:3

Prove that the resultant of two forces acting at point O and represented by vec O B and vec O C is given by 2 vec O D ,where D is the midpoint of BC.

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If 4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+4hat ja n d2 hat i+5 hat j...

    Text Solution

    |

  2. If vec b is a vector whose initial point divides thejoin of 5 hat i...

    Text Solution

    |

  3. Find the value of lambda so that the points P ,Q ,R and S on the sides...

    Text Solution

    |

  4. A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6 at...

    Text Solution

    |

  5. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

    Text Solution

    |

  6. The position vectors of points Aa n dB w.r.t. the origin are vec a=...

    Text Solution

    |

  7. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

    Text Solution

    |

  8. ABCD  is a quadrilateral and  E  is the point of intersection of ...

    Text Solution

    |

  9. A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A...

    Text Solution

    |

  10. Find the vector of magnitude 3, bisecting the angle between the vec...

    Text Solution

    |

  11. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

    Text Solution

    |

  12. If vec r1, vec r2, vec r3 are the position vectors of the collinear ...

    Text Solution

    |

  13. Examine the following vector for linear independence: (1) vec i+ve...

    Text Solution

    |

  14. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

    Text Solution

    |

  15. Let vec a , vec ba n d vec c be three units vectors such that 2 vec a...

    Text Solution

    |

  16. Four non –zero vectors will always be a.  linearly dependent       ...

    Text Solution

    |

  17. A boat moves in still water with a velocity which is k times less t...

    Text Solution

    |

  18. In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively,...

    Text Solution

    |

  19. In a quadrilateral P Q R S , vec P Q= vec a , vec Q R = vec b , vec S ...

    Text Solution

    |

  20. solve the differential equation (1+x^2)dy/dx=x

    Text Solution

    |