If C is the midpoint of AB and P is any point outside AB, then ______ -

If C is the midpoint of AB and P is any point outside AB, then ______

MCQ

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If C is the midpoint of AB and P is any point outside AB, then `underline(overline"PA" + overline"PB" = 2overline"PC")`.

Explanation:

By using triangle law of addition of vectors in triangles PAC and PBC, we have

`overline"PA" + overline"AC" = overline"PC"` and `overline"PB" + overline"BC" = overline"PC"`

⇒ `overline"PA" + overline"AC" + overline"PB" + overline"BC" = overline"PC" + overline"PC"`

⇒ `overline"PA" + overline"PB" + (overline"AC" + overline"BC") = 2overline"PC"`

⇒ `overline"PA" + overline"PB" + (overline"AC" - overline"AC") = 2overline"PC"`

⇒ `overline"PA" + overline"PB" = 2overline"PC"`

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Algebra of Vectors

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