Find the direction cosines of the vector joining the points A(1,2,3)andB(1,2,1), directed from A to B.
Let OACB be a parallelogram with O at the origin andOC a diagonal. Let D be the midpoint of OA˙ using vector methods prove that BDandCO intersect in the same ratio. Determine this ratio.
Given three points are A(−3,−2,0),B(3,−3,1)andC(5,0,2)˙ Then find a vector having the same direction as that of AB and magnitude equal to ∣∣AC∣∣˙
Statement 1: if three points P,QandR have position vectors a,b,andc , respectively, and 2a+3b−5c=0, then the points P,Q,andR must be collinear. Statement 2: If for three points A,B,andC,AB=λAC, then points A,B,andC must be collinear.
If a,bandc are non-coplanar vectors, prove that the four points 2a+3b−c,a−2b+3c,3a+ 4b−2canda−6b+6c are coplanar.
ABC is a triangle and P any point on BC. if PQ is the sum of AP + PB +PC , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.