defence exam Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series Mathematics Vector Algebra Magnitude and Directions of a Vector
Let \(\vec a,\vec b\;and\;\vec c\) be three mutually perpendicular vectors each of unit magnitude. If \(\vec A = \vec a + \vec b + \vec c,\;\vec B = \vec a - \vec b + \vec c\) and \(\vec C = \vec a - \vec b - \vec c,\) then which one of the following is correct?
1
\(\left| {\vec A} \right| > \left| {\vec B} \right| > \left| {\vec C} \right|\)
2
\(\left| {\vec A} \right| = \left| {\vec B} \right| \ne \left| {\vec C} \right|\)
3
\(\left| {\vec A} \right| = \left| {\vec B} \right| = \left| {\vec C} \right|\)
4
\(\left| {\vec A} \right| \ne \left| {\vec B} \right| \ne \left| {\vec C} \right|\)