If D,EandF are three points on the sides BC,CAandAB, respectively, of a triangle ABC such that the CDBD,AECE,BFAF=−1
Fined the unit vector in the direction of vector PQ , where P and Q are the points (1,2,3) and (4,5,6), respectively.
Let r1,r2,r3,,rn be the position vectors of points P1,P2,P3,Pn relative to the origin O˙ If the vector equation a1r1+a2r2++anrn=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a1+a2++˙an=n b. a1+a2++˙an=1 c. a1+a2++˙an=0 d. a1=a2=a3+˙an=0
If a,b,candd are four vectors in three-dimensional space with the same initial point and such that 3a−2b+c−2d=0 , show that terminals A,B,CandD of these vectors are coplanar. Find the point at which ACandBD meet. Find the ratio in which P divides ACandBD˙
If a,bandc are three non-zero non-coplanar vectors, then find the linear relation between the following four vectors: a−2b+3c,2a−3b+4c,3a−4b+5c,7a−11b+15⋅