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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...

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Solution Preview

(a) If the given vectors are orthogonal, their dot product is zero.
Hence we have 1/3 (17α-17)+α/3 (17α^2 )+2(-17α+17/6)=0
This gives (17α-17)+17α^3-102α+17=0
On further simplification, we get 17α^3-85α=0. But α is given to be non zero, we get α^2-5=0
Hence the value of α is ...

Solution Summary

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