Question

(i) Find a vector in the direction of \(\bar r\) = 3E – 4j  that has a magnitude of 9.

(ii) For any three vectors \(\bar a\,,\bar b\,and\, \bar c\), and Prove that \((\bar a + \bar b )+\bar c = a¯+(\bar b + \bar c)\)

(iii) Find a unit vector perpendicular to \(\bar a + \bar b\) and \(\bar a - \bar b\), where \(\bar a\) = i – 3j + 3k and \(\bar b\) and \(\bar c\) = 3E—3j+2k.

Answer 1

(i) Unit vector of magnitude 9

(ii)

(iii)  \(\bar a + \bar b = 4i - 6j + 5k, \bar a - \bar b = -2i + k\)

= i(-6-0) - j(4 + 10) + k(0 - 12)

= -6i - 14j - 12k

Unit vector = \(\frac{-6i -4j - 12k}{\sqrt{36+16+144}}\) = \(\frac{-6i-4j-12k}{\sqrt{376}}\)