Let $$\alpha = \widehat i + 2\widehat j - \widehat k$$, $$\beta = 2\widehat i - \widehat j + 3\widehat k$$ and $$\gamma = 2\widehat i + \widehat j + 6\widehat k$$ be three vectors. If $$\alpha$$ and $$\beta$$ are both perpendicular to the vector $$\delta$$ and $$\delta \,.\,\gamma = 10$$, then what is the magnitude of $$\delta$$ ?

If $$\widehat a$$ and $$\widehat b$$ are two unit vectors then the vector ($$\widehat a$$ + $$\widehat b$$) $$\times$$ ($$\widehat a$$ $$\times$$ $$\widehat b$$) is parallel to

A force $$F = \widehat i + 3\widehat j + 2\widehat k$$ acts on a particle to displace it from the point $$A(\widehat i + 2\widehat j - 3\widehat k)$$ to the point $$B(3\widehat i - \widehat j + 5\widehat k)$$. The work done by the force will be

For any vector a

$${\left| {a \times \widehat i} \right|^2} + {\left| {a \times \widehat j} \right|^2} + {\left| {a \times \widehat k} \right|^2}$$ is equal to ?