We have, #vecA=2i+6j+k=(2,6,1).#
#vecB=(-3,3,3), and, vecC=(5,-1,4).#
#:. 3vecB-vecC=3(-3,3,3)-(5,-1,4),#
#=(-9,9,9)-(5,-1,4),#
#=(-9-5,9-(-1),9-4),#
# rArr 3vecB-vecC=(-14,10,5).#
#:. vecA*(3vecB-vecC)=(2,6,1)*(-14,10,5),#
#=2(-14)+6*10+1.5,#
#=-28+60+5.#
# rArr vecA*(3vecB-vecC)=37.................................................(1).#
(2) : #vecA*(vecBxxvecC).#
#vecBxxvecC=|(i,j,k),(-3,3,3),(5,-1,4)|,#
#=(12-(-3))i-(-12-15)j+(3-15)k,#
#=15i+27j-12k,#
#:. vecBxxvecC=(15,27,-12).#
#:. vecA*(vecBxxvecC)=(2,6,1)*(15,27,-12),#
#=2*15+6*27+1(-12),#
#=30+162-12.#
#rArr vecA*(vecBxxvecC)=180.................................................(2).#
OR,
# vecA*(vecBxxvecC)=|(2,6,1),(-3,3,3),(5,-1,4)|,#
#=2|(3,3),(-1,4)|-6|(-3,3),(5,4)|+1|(-3,3),(5,-1)|,#
#=2(12-(-3))-6(-12-15)+1(3-15),#
#=2.15-6(-27)+1(-12),#
#=30+162-12.#
# rArr vecA*(vecBxxvecC)=180,# as before!..........................#(2).#
(3) : #vecBxx(vecAxxvecC)#
#vecAxxvecC=|(i,j,k),(2,6,1),(5,-1,4)|=(25,-3,-32),#
#:. vecBxx(vecAxxvecC)=|(i,j,k),(-3,3,3),(25,-3,-32)|,#
#=(-96+9)i-(96-75)j+(9-75)k.#
# rArr vecBxx(vecAxxvecC)=-87i-21j-66k..............(3).#
