Let a = 2i + j - 2k and b = i + j. If c is a vector such that a.c = |c|, |c-a| = 2√2 and the angle between

Question

Let \(\vec a = 2\hat i + \hat j - 2\hat k\) and \(\vec b = \hat i + \hat j\). If \(\vec c\) is a vector such that \(\vec a.\vec c = |\vec c|, |\vec c - \vec a| = 2\sqrt2\) and the angle between \(\vec a\times \vec b\) and \(\vec c\) is 30° the \(|(\vec a \times \vec b)\times \vec c| = \)

(a) \(\frac 23\)

(b) \(\frac 32\)

(c) 2

(d) 3

Answer 1

Correct option is (b) \(\frac 32\)