The position vectors of the vertices A,BandC of a triangle are three unit vectors a,b,andc, respectively. A vector d is such that da˙=db˙=dc˙andd=λ(b+c)˙ Then triangle ABC is a. acute angled b. obtuse angled c. right angled d. none of these
If a,bandc are any three non-coplanar vectors, then prove that points l1a+m1b+n1c,l2a+m2b+n2c,l3a+m3b+n3c,l4a+m4b+n4c are coplanar if ⎣⎡l1m1n11l2m2n21l3m3n31l4m4n41⎦⎤=0
Given three non-zero, non-coplanar vectors a,b,and⋅r1=pa+qb+candr2=a+pb+q⋅ If the vectors r1()+2r2and2r1+r2 are collinear, then (P,q) is a. (0,0) b. (1,−1) c. (−1,1) d. (1,1)
If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
Vectors aandb are non-collinear. Find for what value of n vectors c=(n−2)a+bandd=(2n+1)a−b are collinear?