How do you find a unit vector perpendicular to two vectors that is perpendicular to both the vectors u = (0, 2, 1) and v = (1, -1, 1)?

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Answer 1 · 2016-07-22T17:14:15

Reqd. vector#=(3/sqrt14,1/sqrt14,-2/sqrt14)#.

A well-known Property of the Vector Product will be useful in this case.

Given two vectors #vecx and vecy#, we know that, #vecx# x #vecy#

is a vector that is #bot# to both #vecx & vecy#

Therefore, taking #vecu xx vecv = vec w,# say, we get,

#vecw=|(hati, hatj, hatk), (0,2,1), (1,-1,1)|#

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

Now reqd. unit vector, i.e., #hatw# is given by, #vecw/||vecw||#,

where, #||vecw||=sqrt(3^2+1^2+(-2)^2)=sqrt14#

Hence, reqd. vector#hatw=(3/sqrt14,1/sqrt14,-2/sqrt14)#.