What is the unit vector that is normal to the plane containing #( i +k )# and #(2i+ j - 3k)?

1 Answer
May 27, 2016

Answer:

#+-(3hati-3hatj+hatk)/(sqrt19#

Explanation:

If #vecA=hati+hatj and vecB =2hati+hatj-3hatk#
then vectors which will be normal to the plane containing #vec A and vecB# are either#vecAxxvecB or vecBxxvecA# .So we are to find out the unit vectors of these two vector . One is opposite to another.

Now #vecAxxvecB=(hati+hatj+0hatk )xx(2hati+hatj-3hatk)#
#=(1*(-3)-0*1)hati+(0*2-(-3)*1)hatj+(1*1-1*2)hatk#
#=-3hati+3hatj-hatk#

So unit vector of #vecAxxvecB=(vecAxxvecB)/|vecAxxvecB|#
#=-(3hati-3hatj+hatk)/(sqrt(3^2+3^2+1^2))=-(3hati-3hatj+hatk)/(sqrt19#

And unit vector of #vecBxxvecA=+(3hati-3hatj+hatk)/sqrt19#