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Consider the vectors hat i+cos(beta-alp...

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 ka n dcos(alpha-gamma) hat i+cos(beta-gamma) hat k+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`

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