If a = i + j + k, b = 4i + 3j + 4k and c = i + αj + β k are linearly dependent vectors, ​

Question

If \(\vec a = \hat i + \hat j + \hat k,\vec b = 4\hat i + 3\hat j +4\hat k\) and \(\vec c = \hat i + \alpha\hat j + \beta \hat k\) are linearly dependent vectors, and \(|\vec c| = \sqrt 3\), then

(a) \(\alpha = 1, \beta= 1\)

(b) \(\alpha = 1, \beta= \pm1\)

(c) \(\alpha =- 1, \beta= \pm1\)

(d) \(\alpha = \pm1, \beta= 1\)

Answer 1

Correct option is (d) \(\alpha = \pm1, \beta= 1\)