Let a=i^+j^+k^,b=i^−j^+2k^and c=xi^+(x−2)j^−k^. If the vector c lies in the plane of a and b , then x equals
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
If aandb are two non-collinear vectors, show that points l1a+m1b,l2a+m2b and l3a+m3b are collinear if ∣l1l2l3m1m2m3111∣=0.
If a,b,c are non-coplanar vector and λ is a real number, then the vectors a+2b+3c,λb+μcand(2λ−1)c are coplanar when a. μ∈R b. λ=21 c. λ=0 d. no value of λ
If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.
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˙