MCQ
If $a, b $ and $c $ are unit vectors, then $|a - b{|^2} + |b - c{|^2} + |c - a{|^2}$ does not exceed
- A$4$
- ✓$9$
- C$8$
- D$6$
✓
Answer
Correct option: B.
$9$
b
(b) $|a - b{|^2} + |b - c{|^2} + |c - a{|^2}$
(b) $|a - b{|^2} + |b - c{|^2} + |c - a{|^2}$
$ = 2({a^2} + {b^2} + {c^2}) - 2(a.b + b\,.c + c\,.\,a)$
$ = 2 \times 3 - 2(a\,.\,b + b\,.\,c + c\,.\,a)$
$ = 6 - \{ {(a + b + c)^2} - {a^2} - {b^2} - {c^2}\} $$ = 9 - |a + b + c{|^2} \le 9.$
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