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When three quantities a, b and c are in G.P., then the geometric mean "b" is calculated as follows.
Since these quantities are in G.P., the ratio of b/a and the ratio of c/b should give us the same number. In other words these ratios should be equal. That is,
b/a = c/b
On cross multiplying these we have b.b = a.c. That is, b2 = ac.
Example
Find the geometric mean between the two numbers 36 and 40.
If c is the number between these two numbers, then the geometric mean is given by
c2 = (36)(40)
c = √1440 = 37.95
if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 => 1/x 2 +5x+6 = 2/ x 2 +8x +15 => On solving we get x
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Properties of Dot Product u → • (v → + w → ) = u → • v → + u → • w → (cv → ) • w → = v → •(cw → ) = c (v → •w → ) v → • w → = w → • v →
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