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 ?

If the vectors $$a\widehat i + \widehat j + \widehat k$$, $$\widehat i + b\widehat j + \widehat k$$ and $$\widehat i + \widehat j + c\widehat k$$ (a, b, c $$\ne$$ 1) are coplanar, then the value of $${1 \over {1 - a}} + {1 \over {1 - b}} + {1 \over {1 - c}}$$ is equal to

If $$a = \widehat i - \widehat j + \widehat k$$, $$b = 2\widehat i + 3\widehat j + 2\widehat k$$ and $$c = \widehat i + m\widehat j + n\widehat k$$ are three coplanar vectors and $$\left| c \right| = \sqrt 6 $$, then which one of the following is correct?