Find the value of λ so that the points P,Q,R and S on the sides OA,OB,OC and AB, respectively, of a regular tetrahedron OABC are coplanar. It is given that OAOP=31,OBOQ=21,OCOR=31 and ABOS=λ˙ (A) λ=21 (B) λ=−1 (C) λ=0 (D) for no value of λ
Let ABC be triangle, the position vecrtors of whose vertices are respectively i^+2j^+4k^ , -2i^+2j^+k^and2i^+4j^−3k^ . Then DeltaABC is a. isosceles b. equilateral c. right angled d. none of these
A unit vector of modulus 2 is equally inclined to x - and y -axes at an angle π/3 . Find the length of projection of the vector on the z -axis.
If the vectors α=ai^+aj^+ck^,β=i^+k^andγ=ci^+cj^+bk^ are coplanar, then prove that c is the geometric mean of aandb˙