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Let a, b and c be distinct non-negative numbers. If the vectors ahati+ahatj+c hatk, hati+hatk and chati+chatj+bhatk lie in a plane, then c is |
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Answer» the HARMONIC MEAN of a and b `:. |{:(a,a,c),(1,0,1),(c,c,b):}| = 0` On applying `C_(1) rarr C_(1) - C_(2)` , we get `|{:( 0,a,c),(1,0,1),(0,c,b):}| = 0` `rArr -1(ab - c^(2)) = 0 rArr c^(2) = ab` Hence,c is GM of a and b. |
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