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If a line makes angles `alpha,beta,gamma`with the positive direction ofcoordinate axes, then write the value of `sin^2alpha+sin^2beta+sin^2gammadot` |
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Answer» Direction cosines of the given line is `cos alpha, cos beta,cos gamma`. Also, we know, sum of squares of direction cosines is `1`. `:. cos^2alpha+cos^2beta+cos^2gamma = 1` `=>1-sin^2alpha+1-sin^2beta+1-sin^2gamma = 1` `=>sin^2alpha+sin^2beta+sin^2gamma = 3-1` `=>sin^2alpha+sin^2beta+sin^2gamma = 2` So, required value is `2`. |
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