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Show that the scalarproductof two vectors obeys the law of disrtrictive |
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Answer» SOLUTION :According to figure, `Ovec(P)= vec(A ) , O vec (Q) = vec(B) and vec(QR) = vec(C )` Now `vec(A) . (vec(B) +vec(C )) ` = (Magnitude of `vec(A)) xx ` ( Componentof `vec(B) +vec(C )` along the DIRCTION of `vec(A)`) `= |vec(A) |` (ON) ` = |vec(A)| (OM +MN)` ` = | vec(A)| OM +|vec(A)|MN` ` :. vec(A) . (vec(B) + vec(C )) = |vec(A)|xx (" component of" vec(B)" along" vec(A)) +|vec(A)|` (component of `vec(C ) `along `vec(A)`) ` :. vec(A) . (vec(B) +vec (C )) = vec(A) . vec(B) +vec(A) .vec(C )` |
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