Let Δ P Q R be a triangle. Let a → =   Q R → ,     b → =   R P →   a n d   c → =   P Q → . If a → = 12 ,   b → = 4 3 and b →   ⋅   c → = 24 , then which of the following is…

Question

Let &#916; P Q R be a triangle. Let a &#8594; = &#160; Q R &#8594; , &#160; &#160; b &#8594; = &#160; R P &#8594; &#160; a n d &#160; c &#8594; = &#160; P Q &#8594; . If a &#8594; = 12 , &#160; b &#8594; = 4 3 and b &#8594; &#160; &#8901; &#160; c &#8594; = 24 , then which of the following is (are) true ?

Aicharya · Accepted Answer

a → = 12 , b → = 4 3 , b . → c → = 24 a → + b → + c → = 0 (Sides of triangle) b → + c → = - a → b → + c → . b → + c → = - a → . - a → b → 2 + c → 2 + 2 b → . c → = a → 2 48 + c → 2 + 2 × 24 = 12 2 c → 2 = 48 c → 2 2 - a → = 48 2 - 12 = 12 c → 2 2 + a → = 48 2 + 12 = 36 a → × b → + c → × a → = a → × b → - a → × c → = a → × b → - c → a → = - b → - c → = - b → - c → × b → - c → = b → - c → × b → + c → = 2 b → × c → = 2 b → 2 c → 2 - b → . c → 2 = 2 48 × 48 - 24 2 = 2 × 24 4 - 1 = 48 3 a → + b → = - c → a → + b → . a → + b → = - c → . - c → a → 2 + b → 2 + 2 a → . b → = c → 2 a → . b → = - a → 2 2 = - 12 2 2 = - 72

Let Δ P Q R be a triangle. Let a → =   Q R → ,     b → =   R P…

Solution

Let &#916; P Q R be a triangle. Let a &#8594; = &#160; Q R &#8594; , &#160; &#160; b &#8594; = &#160; R P…

Solution

Let Δ P Q R be a triangle. Let a → = Q R → , b → = R P…