Question

5. Given vectors A 2âx - âv +3âz and B = 3âx - 2â^, find vector C whose magnitude is 6 and direction is perpendicular to both A and B. Hint C is orthogonal to both A and B 6. Determine Az so that vectors A = -2âx 3ây +A2âz and B = 3âx + ây +3âz are orthogonal

Answer 1

Wo Know, the anlas ktween two uKetors and is given b COLaz If tho vetox s are orthe genol then Ihis ives Thystuo vectors v tho onal are if O and Let then is orthoonal to A and B A.20 B.C and which gives, 2-C+3 c3= O 34209 O TerBITO

gives Ox3 Now, + ラC2ニ 132 also fom cis 6 Since the magnitude of S0 6 169 c2 7 36 A+ 169 t9)= 36 36 x9 162 182 91 2 91 13 39

30, c4an c ='q&a caz + q ant 39 911 92 39 + 6. Sincs A and B tho gonal, then A B zántsayt Asi, + os6)- -26+3a+ 6 3+ 3 A 0 Az 2 NY Hen ce,