Question

If the vector $\vec { a }$ = (c log₂ x) – 6 $\hat { \mathrm { j } }$ + 3 $\hat { \mathbf { k } }$ and

= (log₂ x) + 2 $\hat { \mathrm { j } }$ + (2c log₂ x) make an obtuse angle for any x Ī (0, ) then the interval to which 'c' belongs is –

• A. (0, )
• B. (– , 0)
• C. (– 4/3, 0)
• D. (–1, 0) Č (0, 2/3)

Answer 1

Answer: (C)

(– 4/3, 0)

Answer 2

For vectors and $\overrightarrow { \mathrm { b } }$ to be inclined at an obtuse angle

. $\overrightarrow { \mathrm { b } }$ < 0 , x Ī (0, )c(log₂ x)² – 12 + 6 c log₂ x < 0 " x Ī

(0, )

cy² + 6 < cy – 12 <0 y Ī R y

= log₂ xc < 0 and 36 c² + 48 c < 0

c < 0 c (3c + 4)

< 0c Ī (– 4/3, 0)