If a, b and c are unit vectors, then ∣a−b∣2+∣b−c∣2+∣c−a∣2 does not exceed
Explanation
Concept:
A unit vector is a vector whose magnitude is 1.
Calculation:
Given that ∣a−b∣2+∣b−c∣2+∣c−a∣2,
since a, b, and c are unit vectors so a2=b2=c2=1
Expanding the above expression,
(a2+b2−2ab)+(b2+c2−2bc)+(c2+a2−2ac)
⇒2(a2+b2+c2)−(2ab+2bc+2ac)
⇒2(1+1+1)−{(a+b+c)2−(a2+b2+c2)}
⇒6−{(a+b+c)2−(1+1+1)}
\Rightarrow 9 - (a + b + c)^2 < 9
Explanation
Concept:
A unit vector is a vector whose magnitude is 1.
Calculation:
Given that ∣a−b∣2+∣b−c∣2+∣c−a∣2,
since a, b, and c are unit vectors so a2=b2=c2=1
Expanding the above expression,
(a2+b2−2ab)+(b2+c2−2bc)+(c2+a2−2ac)
⇒2(a2+b2+c2)−(2ab+2bc+2ac)
⇒2(1+1+1)−{(a+b+c)2−(a2+b2+c2)}
⇒6−{(a+b+c)2−(1+1+1)}
\Rightarrow 9 - (a + b + c)^2 < 9
