Concept:For two vectors \(\vec m \ and \ \vec n \) to be collinear,? \(\vec m\; = \;? \vec n\) where ? is a scalar.Calculation:Given that, the vectors \(4\hat i + \hat j - 3\hat k\) & \(p\hat i + q\hat j - 2\hat k\) are collinear.Since two vectors \(\vec m \ and \ \vec n \) are collinear then \(\vec m\; = \;? \vec n\) where ? is a scalar.? \(4\hat i + \hat j - 3\hat k\;\ = ? × (\;p\hat i + q\hat j - 2\hat k)\)? \(4\hat i + 1\hat j - 3\hat k\;\ = ? p \hat i + ?q \hat j - 2? \hat k\)? ?p = 4, ?q = 1 and -2? = -3? ? = 3/2 So, by substituting ? = 3/2 in ?p = 4 and ?q = 1, we get? (3/2)p = 4 and (3/2)q = 1? p = 8/3 and q = 2/3? \(\frac{8}{3}, \frac{2}{3}\)is the correct answer.