If a and b are unit vectors and $$\theta$$ is the angle between them, then what is $${\sin ^2}\left( {{\theta \over 2}} \right)$$ equal to ?

Consider the following equations for two vectors a and b.

1. $$(a + b).(a - b) = {\left| a \right|^2} - {\left| b \right|^2}$$

2. $$(\left| {a + b} \right|)(\left| {a - b} \right|) = {\left| a \right|^2} - {\left| b \right|^2}$$

3. $$\left| {a\,.\,b} \right| + \left| {a \times b} \right| = {\left| a \right|^2}{\left| b \right|^2}$$

Which of the above statements are correct?

If the magnitude of the sum of two non-zero vectors is equal to magnitude of their difference, then which one of the following is correct?

What is the scalar projection of

$$a = \widehat i - 2\widehat j + \widehat k$$ on

$$b = 4\widehat i - 4\widehat j + 7\widehat k$$ ?