How do you find a unit vector orthogonal to both vectors (1, -3, 2) and (-1, 2, 3)?

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Answer 1 · 2017-02-01T18:57:43

#"The Reqd. Unit Vector="1/sqrt195(-13,-5,-1).#

We know from Vector Geometry that #vecx xx vecy# is a vector

which is orthogonal to both #vecx and vecy.#

The desired Unit Vector , then, can be obtained as

#(vecx xx vecy)/||vecx xx vecy||#

#"Now, "(1,-3,2) xx (-1,2,3)=|(i,j,k),(1,-3,2),(-1,2,3)|#

#=(-13,-5,-1)," so that, "||((-13,-5,-1))||=sqrt195#

#"Therefore, the Reqd. Unit Vector="1/sqrt195(-13,-5,-1).#