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

1 Answer
P dilip_k
May 27, 2016

+-(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 eithervecAxxvecB 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

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