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Alpha, Beta and Gamma diversity are type...

Alpha, Beta and Gamma diversity are types of genetic diversity.

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Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat k ,cos(alpha-beta) hat i+ hat j+"cos"(gamma-beta) hat k and cos(alpha-gamma) hat i+cos(beta-gamma) hat j+a hat k where alpha,beta , and gamma are different angles. If these vectors are coplanar, show that a is independent of alpha,beta and gamma