What is the cross product of #[2,-1,2]# and #[4,-3,1] #?

1 Answer

Answer:

the cross product
#a#x#b=+5i+6j-2k#

Explanation:

Let vector #a=2*i-1*j+2*k# and #b=4*i-3*j+1*k#

The formula for cross product

#a#x#b=[(i,j,k),(a_1,a_2,a_3),(b_1,b_2,b_3)]#

#a#x#b=+a_2b_3i+a_3b_1j+a_1b_2k-a_2b_1k-a_3b_2i-a_1b_3j#

Let us solve the cross product

#a#x#b=[(i,j,k),(2,-1,2),(4,-3,1)]#

#a#x#b=#

#+(-1)(1)i+(2)(4)j+(2)(-3)k-(-1)(4)k-(2)(-3)i-(2)(1)j#

#a#x#b=-1*i+6i+8j-2j-6k+4k#

#a#x#b=+5i+6j-2k#

God bless...I hope the explanation is useful.