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

1 Answer
Jane
Mar 17, 2018

We know that if #vec C= vec A × vec B# then #vec C# is perpendicular to both #vec A# and #vec B#

So,what we need is just to find the cross product of the given two vectors.

So,#(hati+hatj-hatk)×(hati-hatj+hatk)=-hatk-hatj-hatk+hati-hatj-i=-2(hatk+hatj)#

So,the unit vector is #(-2(hatk+hatj))/(sqrt(2^2 +2^2))=-(hatk+hatj)/sqrt(2)#

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