What is the unit vector that is orthogonal to the plane containing # <3, -6, 2> # and # <3, 2, 1> #?

1 Answer
Feb 21, 2016

Answer:

#(-10/sqrt 685*i+3/sqrt 685*j+24/sqrt 685.k)#

Explanation:

#"step 1:Find cross product of two vector"#
#"the cross product of two vector in the same plane is perpendicular to the plane"#
#"let "vec C=vec A X vec B#
#vec C=i(a_y*b_z-a_z*b_y)-j(a_x*b_z-a_z*b_x)+k(a_x*b_y-a_y*b_x)#
#vec c=i(-10)-j(-3)+k(24)#
#vec C=-10i+3j+24k#
#"step 2:Find magnitude of the vector of " vec C#
#||c||=sqrt((-10)^2+3^2+24^2)#
#||c||=sqrt (100+9+576)#
#||c||=sqrt 685#
#step 3:" use : vec C /||c||#
#(-10i+3j+24k)/sqrt 685#
#(-10/sqrt 685*i+3/sqrt 685*j+24/sqrt 685.k)#