If a + 2b + 3c = 0 and a $$\times$$ b + b $$\times$$ c + c $$\times$$ a = $$\lambda$$ (b $$\times$$ c), then what is the value of $$\lambda$$ ?

If the vectors K and A are parallel to each other, then what is kK $$\times$$ A equal to ?

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 ?