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Vector Algebra

Question
CBSEENMA12034041
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A point P divides a line segment AB in the ratio A : 1. Give the values of A for which
P lies in between AB and 
(i) nearer A than B    (ii) nearer B than A

Solution
Since P lies in between AB and P is nearer A than B.
therefore space space space space AP space less than thin space BP space space space straight i. straight e. space AP over BP less than 1 therefore space space space straight lambda space less than space 1. space space space Also space straight lambda space greater than 0 therefore space space space 0 space less than space straight lambda space less than space 1.
If P is nearer to B than A, then AP greater than BP space space straight i. straight e. space space AP over BP greater than 1 space comma space space straight i. straight e. space space space space straight lambda space greater than space 1.

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