What is the cross product of #[3, 2, 5]# and #[-1, 2, 2] #?

1 Answer

Answer:

#color(blue)(a " x " color(blue)(b=-6i-11j+8k)#

Explanation:

Let vector #a=3*i+2*j+5*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),(3, 2, 5),(-1, 2, 2)]#

#a#x#b=#

#+(2)(2)i+(5)(-1)j+(3)(2)k-(2)(-1)k-(5)(2)i-(3)(2)j#

#a#x#b=+4*i-10i-5j-6j+6k+2k#

#a#x#b=-6i-11j+8k#

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