JEE Advance - Mathematics (1998 - No. 6)
If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vectors and $$\left| c \right| = \sqrt 3 ,$$ then
$$\alpha = 1,\,\,\beta = - 1$$
$$\alpha = 1,\,\,\beta = \pm 1$$
$$\alpha = - 1,\,\,\beta = \pm 1$$
$$\alpha = \pm 1,\,\,\beta = 1$$