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

Similar Questions

Explore conceptually related problems

The value of the lambda so that P,Q,R, S on the sides OA,OB,OC and AB of a regular tetrahedron are coplanar.When (OP)/(OA)=(1)/(3);(OQ)/(OB)=(1)/(2) and (OS)/(AB)=lambda is(A)lambda=(1)/(2)(B)lambda=-1(C)lambda=0(D)lambda=2

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

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

O is any point on the diagonal B D of the parallelogram A B C Ddot Prove that a r( O A B)=a r( O B C)

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot

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 the points A(2,3,-4), B(1,-2,3) and C (3,lambda,-1) are colliner, then value of lambda is

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

ABC if median from B and C are perpendicular then the value of cot B + cot C can be 0(1)/(2) O -(1)/(2) O (2)/(3) O -(2)/(3)