Question

If a, b and c are unit vectors satisfying |a – b|² + |b – c|² + |c – a|² = 9, then |2a + 5b + 5c| is.

Answer 1

Given, |a – b|² + |b – c|² + |c – a|² = 9

Now, |2a + 5b + 5c| = |2a + 5(b + c)|

= |2a + 5(–a)|

= |– 3(a)|

= |– 3| |a|

= 3