L and M are two points with position vectors 2 a → − b → and a → + 2 b → respectively. The position vector of the point N which divides the line segment L M in the ratio 2 : 1 externally is

Question

L and M are two points with position vectors 2 a → − b → and a → + 2 b → respectively. The position vector of the point N which divides the line segment L M in the ratio 2 : 1 externally is, 3 b →, 4 b →, 5 b →, 3 a → + 4 b →

MARKS App · Accepted Answer

Since point N n ¯ divides LM in ratio 2:1 externally ⇒ n ¯ = 2 ( m ¯ ) − l ¯ 2 − l (Using section formula) ⇒ n ¯ = 2 ( a ¯ + 2 b ¯ ) − ( 2 a ¯ − b ¯ ) ⇒ n ¯ = 2 a ¯ + 4 b ¯ − 2 a ¯ + b ¯ ⇒ n ¯ = 5 b ¯

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