A force $$F = 3\widehat i + 2\widehat j - 4\widehat k$$ is applied at the point (1, $$-$$ 1, 2). What is the moment of the force about the point (2, $$-$$1, 3) ?

What is a vector of unit length orthogonal to both the vectors $$\widehat i + \widehat j + \widehat k$$ and $$2\widehat i + 3\widehat j - \widehat k$$ ?

If a, b and c are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

What is the area of the parallelogram having diagonals $$3\widehat i + \widehat j - 2\widehat k$$ and $$\widehat i - 3\widehat j + 4\widehat k$$ ?