If the magnitude of difference of two unit vectors is $$\sqrt 3 $$, then the magnitude of sum of the two vectors is

If the vectors $$\alpha \widehat i + \alpha \widehat j + \gamma \widehat k$$, $$\widehat j + \widehat k$$ and $$\gamma \widehat i + \gamma \widehat j + \beta \widehat k$$ lie on a plane, where $$\alpha$$, $$\beta$$ and $$\gamma$$ are distinct non-negative numbers, then $$\gamma$$ is

The vectors a, b, c and d are such that a $$\times$$ b = c $$\times$$ d and a $$\times$$ c = b $$\times$$ d. Which of the following is/are correct?

1. (a $$-$$ d) $$\times$$ (b $$-$$ c) = 0

2. (a $$\times$$ b) $$\times$$ (c $$\times$$ d) = 0

Select the correct answer using the code given below.

Let $$a = \widehat i + \widehat j$$, $$b = 3\widehat i + 4\widehat k$$ and $$b = c + d$$, where c is parallel to a and d is perpendicular to a.

What is c equal to ?