Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The vector 
is rotated through an angle of cos –1 
and doubled in magnitude, then it becomes 
. The value of ' x ' CANNOT be :
A
− 
B
C
D
2
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,c)
= 
⇒ 
= 4 
⇒ 16 + (4x – 2) 2 + 4 = 4 (1 + x 2 + 9) ⇒ 20 + 16x 2 + 4 – 16x = 4 + 4x 2 + 36
⇒ 12x 2 – 16x – 16 = 0 ⇒ 3x 2 – 4x – 4 = 0
⇒ x = 2 , – 
...(i)
angle between 
and 
is cos θ = 
= 
⇒ 
= 
= 
⇒ 11 x 2 + 110 = 70 + 28 x 2 – 14x
⇒ 17x 2 – 14x – 40 = 0 ∴ x = 2, – 
.......(ii)
from (i) and (ii)
x = 2
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