If the angle between `2hati+ 2hatj- hatk` and vector `hati + chatk` is acute, then the maximum value of c is :

Answer

2

Explanation

`cos theta = (vecA.vecB)/(|vecA||vecB|) =- ((2hati + 2hatj + hatk ) xx (hati + chatk))/(sqrt((2)^(2) + (2)^(2) + (-1)^(2) .sqrt(1+ c^(2))))`
`= (2-c)/(3sqrt(1 + c^(2)))`
If `theta` is acute , ` cos theta` is positive.
`" "cos theta ge 0`
`" "2cge 0`
`" "2 le c`
`" "c le 2`
Thus, the maximum value of c is 2.