Question #a42a8

1 Answer
Mar 18, 2017

Let

#veca=hati-2hatj+hatk#
and
#vecb=3hati+hatj-2hatk#

The cross product of these two vectors (# veca and vecb#) is a vector #vecc# perpendicular to both as shown in the figure below

google image

So
#vecc =veca xxvecb=[(hati,hatj,hatk),(hati,-2hatj,hatk),(3hati,hatj,-2hatk)]#

#=((-2)*(-2)-1*1)hati+(1*3-1*(-2))hatj+(1*1-3*(-2))hatk#

#=3hati+5hatj+7hatk#

So unit vector of #vecc=vecc/abs(vecc)#

#=(3hati+5hatj+7hatk)/sqrt(3^2+5^2+7^2)#

#=(3hati+5hatj+7hatk)/sqrt83color(red)(->"option (2)")#