Find the least positive integral value of x for which the angle between vectors a→=xi^−3j^−k^ and  b→=2xi^+xj^−k^ is acute

Let a→=xi^−3j^−k^ and b→=2xi^+xj^−k^ be the adjacent sides of the parallelogram Now angle between a→ and b→ is acute, i.e., |a→+b→|>|a→−b→|⇒|3xi^+(x−3)j^−2k^|2>|−xi^−(x+3)j^|2or  9x2+(x−3)2+4>x2+(x+3)2or  8x2−12x+4>0or  2x2−3x+1>0or (2x−1)(x−1)>0⇒ x<1/2 or x>1Hence, the least positive integral value is 2.