Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The value(s) of α ∈ [0, 2 π ] for which vector 
makes an obtuse angle with the z-axis and the vectors 
and 
= (tan α ) 
+ (tan α ) 
– 3 
are orthogonal, is/are
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Since 
makes obtuse angle with z-axis
∴ 
< 0 i.e. sin 2 α < 0
∴ either 
< α < π or 
< α < 2 π ......(i)
since 
and 
are orthogonal
∴ tan 2 α – tan α – 6 = 0 i.e. tan α = 3, –2 ......(ii)
from (i) and (ii), we get
tan α = – 2 ∴ α = π – tan –1 2 or α = 2 π – tan –1 2
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