If bandc are two-noncollinear vectors such that a∣∣(b×c), then prove that (a×b).(a×c) is equal to ∣a∣2(bc˙)˙
Two forces AB and AD are acting at vertex A of a quadrilateral ABCD and two forces CB and CD at C prove that their resultant is given by 4EF , where E and F are the midpoints of AC and BD, respectively.
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.
Column I, Column II Collinear vectors, p.a Coinitial vectors, q. b Equal vectors, r. c Unlike vectors (same intitial point), s. d
Show that the points A(6,−7,0),B(16,−19,−4),C(0,3,−6)and D(2,−5,10) are such that ABandCD interesect at the point P(1,−1,2)˙
A unit vector of modulus 2 is equally inclined to x - and y -axes at an angle π/3 . Find the length of projection of the vector on the z -axis.
If ABCD is quadrilateral and EandF are the mid-points of ACandBD respectively, prove that AB+AD +CB +CD =4 EF˙
Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.