​ Consider bar a = i + 2j – 3k, bar b = 3i – j + 2k, bar c = 11i + 2j ​1. ​ Find bar (a+b) and bar (a.b) . ​

Question

Consider \(\bar a\) = i + 2j – 3k, \(\bar b\) = 3i – j + 2k, \(\bar c\) = 11i + 2j

1. Find \(\bar a\) + \(\bar b\) and \(\bar a\).\(\bar b\) 
2. Find the unit vector in the direction of \(\bar a\) + \(\bar b\).
3. Show that \(\bar a\) + \(\bar b\). and  \(\bar a\) - \(\bar b\). are orthogonal.

Answer 1

1.

2. Unit vector in the direction of

3. We have,

Therefore, they are orthogonal.