Question

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Answer 1

Given,

{ Note: all terms are in vector form }

$o p_{1} + p_{1} p_{2} + p_{2} p_{3} = p_{3} p_{4} = o \\ \\ o p_{1} + p_{1} p_{2} + p_{2} p_{3} + p_{3} p_{4} = o$

prove:

that P4 coincides with O .

Solution:

{ by triangle law }

$o p_{1} + p_{1} p_{2} + p_{2} p_{3} + p_{3} p_{4} = o \\</em><em>=</em><em>></em><em> (o p_{1} + p_{1} p_{2}) + p_{2} p_{3} + p_{3} p_{4} = o \\ o p_{2} + p_{2} p_{3} + p_{3} p_{4} = o \\ </em><em>=</em><em>></em><em> (o p_{2} + p_{2} p_{3}) + p_{3} p_{4} = o \\ o p_{3} + p_{3} p_{4} = o \\ = > o p_{4} = o \\ \\ p_{4} \: coincides \: with \: o \\ hence \: proved.$

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Answer 2

Answer:

all terms are in vector form