1. A conducting filamentary triangle joins points $$ \mathrm{A}(3,1,1), \mathrm{B}(5,4 $$, 2), and $$ \mathrm{C}(1,2,4) $$. The segment AB carries a current of 0.2 A in the AB direction. There is present a magnetic field $$ \mathrm{B}=0.2 \mathrm{ax}-0.1 \mathrm{a} $$, +0.3 az T . Find: (a) the force on segment BC ; (b) the force on the triangular loop; (c) the torque on the loop about an origin at $$ \mathrm{A} ;(\mathrm{d}) $$ the torque on the loop about an origin at C .

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(a) The force on segment BC is $$ -0.64 \, 	ext{N} $$ in the direction opposite to the cross product. (b) The force on the triangular loop is $$ 0 \, 	ext{N} $$. (c) The torque on the loop about an origin at A is $$ 0 \, 	ext{Nm} $$. (d) The torque on the loop about an origin at C is $$ 0 \, 	ext{Nm} $$.

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