Let a,b,andc be three non coplanar unit vectors such that the angle between every pair of them is 3π. If a×b+b×x=pa+qb+rc where p,q,r are scalars then the value of q2p2+2q2+r2 is
If a,b,andc be three non-coplanar vector and aprime,bprimeandc′ constitute the reciprocal system of vectors, then prove that r=(ra˙′)a+(rb˙′)b+(rc˙′)c r=(ra˙′)a′+(rb˙′)b′+(rc˙′)c′
A ship is sailing towards the north at a speed of 1.25 m/s. The current is taking it towards the east at the rate of 1 m/s and a sailor is climbing a vertical pole on the ship at the rate of 0.5 m/s. Find the velocity of the sailor in space.
If A,B,C,D are four distinct point in space such that AB is not perpendicular to CD and satisfies ABC˙D=k(∣∣AD∣∣2+∣∣BC∣∣2−∣∣AC∣∣2−∣∣BD∣∣2), then find the value of k˙
Let ABCD be a p[arallelogram whose diagonals intersect at P and let O be the origin. Then prove that OA+OB+OC+OD=4OP˙
Statement 1: If uandv are unit vectors inclined at an angle αandx is a unit vector bisecting the angle between them, then x=(u+v)/(2sin(α/2)˙ Statement 2: If DeltaABC is an isosceles triangle with AB=AC=1, then the vector representing the bisector of angel A is given by AD=(AB+AC)/2.