Vector Algebra

The least positive integral value of , for which the angle between the vectors i-2 j+2 k and i+2 j-2 k is acute, is .

Answer

5

Solution

∵ angle is acute ⇔ dot product >0 (vectors are never parallel here)

2-4 -4>0 ⇒ ( -2)2>8

⇒ >2+2 2 4.83 or <2-2 2 (negative)

∴ least positive integer =5

Answer: 5