InterviewSolution
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InterviewSolution
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यदि हो इकाई सदिशों `veca " तथा" vecb ` के बीच का कोण `theta ` हो तो सिद्ध कीजिए की - ` sin (theta)/(2) = (1)/(2) |veca - vecb|` |
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Answer» `because |veca| = 1 "तथा " |vecb| = 1` ` therefore vec a . vecb = (1)(1) costheta = cos theta ` …(1) ` |veca - vecb|^(2) = (veca - vecb)^(2)` ` = (veca)^(2) + (vecb)^(2) - 2(hata . hatb)` `= |veca|^(2) + |vecb|^(2) - 2cos theta ` (समीकरण (1) से ) `= 1 + 1 - 2costheta = 2 - 2 (1 - sin^(2) (theta)/(2))` ` 4sin^(2) (theta)/(2)` ` therefore 2sin (theta)/(2) = |veca - vecb|` ` rArr sin (theta)/(2) = (1)/(2) |veca - vecb|` . |
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