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

$The Reqd. Unit Vector= \frac{1}{\sqrt{195}} (- 13, - 5, - 1) .$ $"The Reqd. Unit Vector="1/sqrt195(-13,-5,-1).$

We know from Vector Geometry that $\to x \times \to y$ $vecx xx vecy$ is a vector

which is orthogonal to both $\to x and \to y .$ $vecx and vecy.$

The desired Unit Vector , then, can be obtained as

$\frac{\to x \times \to y}{∣ ∣ ∣ ∣ \to x \times \to y ∣ ∣ ∣ ∣}$ $(vecx xx vecy)/||vecx xx vecy||$

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

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

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