If a,b,c are unit vectors such that a+b+c=0find the value of a⋅b+b⋅c+c⋅a.
A straight line L cuts the lines AB,ACandAD of a parallelogram ABCD at points B1,C1andD1, respectively. If (AB)1,λ1AB,(AD)1=λ2ADand(AC)1=λ3AC, then prove that λ31=λ11+λ21 .
aandb form the consecutive sides of a regular hexagon ABCDEF˙ Column I, Column II If CD=xa+yb, then, p. x=−2 If CE=xa+yb, then, q.x=−1 If AE=xa+yb, then, r. y=1 AD=−xb, then, s.y=2
In a trapezium, vector BC=αAD˙ We will then find that p=AC+BD is collinear withAD˙ If p=μAD, then which of the following is true? a. μ=α+2 b. μ+α=2 c. α=μ+1 d. μ=α+1
Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.