Area of a rectangle having vertices A, B, C and D with position vectors −i^+21j^+4k^,i^+21j^+4k^,i^−21j^+4k^ and −i^−21j^+4k^ respectively is
(A) 1/2 (B) 1 (C) 2 (D) 4
Let a,bandc be unit vectors such that a+b−c=0. If the area of triangle formed by vectors aandbisA, then what is the value of 4A2?
In a △OAB,E is the mid point of OB and D is the point on AB such that AD:DB=2:1 If OD and AE intersect at P then determine the ratio of OP:PD using vector methods
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
The position vectors of the vertices A,B,andC of a triangle are i^+j^,j^+k^andi^+k^ , respectively. Find the unite vector r^ lying in the plane of ABC and perpendicular to IA,whereI is the incentre of the triangle.
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)
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.