Without expanding the determinants, prove that `|103 115 114 111 108 106 104 113 116|+|113 116 104 108 106 111 115 114 103|=0`

Without expanding the determinants Prove that |{:(103,,115,,114),(111,,108,,106),(104,,113,,116):}| + |{:(113,,116,,104),(108,,106,,111),(115,,114,,103):}|=0

Without expanding prove that Delta ={:[( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) ]:} =0

Covalent radii (in A) for some elements of different groups and periods are listed below. Plot these values against atomic number. From the plot, explain the variation along a period and a group. 2^nd group elements : Be (0.89), Mg (1.36), Ca (1.74), Sr (1.91) Ba(1.98) 17^th group elements : F (0.72), CI (0.99), Br(1.14). T (1.33) 3^rd Period elements : Na(1.57), Mg(1.36). AI (1.25), Si(1.17). P(1.10), S(1.04). C1(0.99) 4^th period elements : K(2.03), Ca(1.74). Sc(1.44). Ti(1.32), V(1.22), Cr(1.17), Mn(1.17) Fe(1.17). Co(1.16). Ni(1.15). Cu(1.17). Zn(1.25), Ga(1.25). Ge(1.22). As(1.21). Se(1.14). Br(1.14)