Question

lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is ______.

Options

• `-(3a^2)/2`

• `(3a^2)/2`

• `a^2/3`

• `-a^2/3`

Answer 1

lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is `underlinebb(-(3a^2)/2)`.

Explanation:

`bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)`

= (a) (a) cos 120° + (a) (a) cos 120° + (a) (a) cos 120°

= `a^2 (-1/2) + a^2 (-1/2) + a^2 (-1/2)`

= `-a^2/2 - a^2/2 - a^2/2`

= `-(3a^2)/2`