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

1 Answer

Answer:

#a#x#b=-10i-8j+3k#

Explanation:

Let vector #a=2*i-1*j+4*k# and #b=-1*i+2*j+2*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, 4),(-1, 2, 2)]#

#a#x#b=#

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

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

#a#x#b=-10i-8j+3k#

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