Consider the following statements.

1. The magnitude of a $$\times$$ b is same as the area of a triangle with sides a and b.

2. if a $$\times$$ b = 0, where a $$\ne$$ 0, b $$\ne$$ 0, then a = $$\lambda$$ b.

Which of the above statements is/are correct?

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?