Let a = -i - j + k, a.b =1 and a x b = i - j. then a - 6b is equal to

Question

Let \(\vec a = -\hat i - \hat j + \hat k, \vec a.\vec b=1 \) and \(\vec a \times \vec b = \hat i - \hat j\). Then \(\vec a - 6\vec b\) is equal to 

(1) \(3(\hat i - \hat j - \hat k)\)

(2) \(3(\hat i + \hat j + \hat k)\)

(3) \(3(\hat i - \hat j+ \hat k)\)

(4) \(3(\hat i + \hat j - \hat k)\)

Answer 1

Correct option is (2) \(3(\hat i + \hat j + \hat k)\)