​ Consider the vector bar p = 2i – j + k. Find two vectors and such that bar p, bar q and bar r are mutually perpendicular. ​

Question

Consider the vector \(\bar p\) = 2i – j + k. Find two vectors \(\bar q\) and \(\bar r\) such that \(\bar p,\bar q\)and \(\bar r\) are mutually perpendicular.

Answer 1

Find a vector \(\bar q\) such that \(\bar p.\bar q\) = 0, for this use any \(\bar q\) whose two components are randomly selected. 

Let \(\bar q\) = 2i + 2j + xk 

 \(\bar p.\bar q\) = (2i – j + k) . (2i + 2 j + xk) = 0

⇒ 4 – 2 + x = 0 ⇒ x = -2

= 6j + 6k.