Mumbai University > Electronics and Telecommunication > Sem 4 > Applied Maths 4

Marks: 5M

Year: May 2015

Let a = [1,1,0] & b = [0,1,1]

The cross product of a $\times$ b is orthogonal to both a & b.

$$\therefore a \times b = \begin{vmatrix} i & j & k \\ 1 & 1 & 0 \\ 0 & 1 & 1\end{vmatrix} \\ = i(1) - j(1) + k(1) \\ = i - j + k$$

A unit vector is a vector whose length is 1.

Therefore, the unit vector is

$$= \frac{i - j + k}{\sqrt{1^2 + (-1)^2 + 1^2}} \\ = \frac{i - j + k}{\sqrt{3}} \\ = \bigg[\frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\bigg]$$