A,B,CandD have position vectors a,b,candd, respectively, such that a−b=2(d−c)˙ Then a. ABandCD bisect each other b. BDandAC bisect each other c. ABandCD trisect each other d. BDandAC trisect each other
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.
If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.
Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.
If aandb are two unit vectors and θ is the angle between them, then the unit vector along the angular bisector of a and b will be given by a. cos(θ/2)a−b b. 2cos(θ/2)a+b c. 2cos(θ/2)a−b d. none of these
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.
A pyramid with vertex at point P has a regular hexagonal base ABCDEF , Positive vector of points A and B are i^andi^+2j^ The centre of base has the position vector i^+j^+3k^˙ Altitude drawn from P on the base meets the diagonal AD at point G˙ find the all possible position vectors of G˙ It is given that the volume of the pyramid is 63 cubic units and AP is 5 units.