# Orthogonal vectors

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Dot and cross product (3P+3P+2P)

Determine all values ...such that the vectors...are orthogonal.

Determine a unit vector...that is orthogonal to both...

https://brainmass.com/math/calculus-and-analysis/multivariate-value-calculus-203656

#### Solution Preview

(a) If the given vectors are orthogonal, their dot product is zero.

Hence we have 1/3 (17Î±-17)+Î±/3 (17Î±^2 )+2(-17Î±+17/6)=0

This gives (17Î±-17)+17Î±^3-102Î±+17=0

On further simplification, we get 17Î±^3-85Î±=0. But Î± is given to be non zero, we get Î±^2-5=0

Hence the value of Î± is ...

#### Solution Summary

This provides examples of working with orthogonal vectors. Multivariate value calculus is examined.

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