The resultant of two vectors 
and 
is perpendicular to 
and its magnitude is half that of 
. The angle between vectors 
and 
is) _______ 
.
Text Solution
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To solve this problem, we'll analyze the conditions given about the vectors 
and 
, and their resultant 
.
Given:
(i) 
is perpendicular to 
.
(ii) The magnitude of 
is half that of 
:
Approach:
We know that if 
is perpendicular to 
, then their dot product is zero:
Substitute 
:
Next, we use the second condition involving magnitudes:
Finally, substitute this back into the cosine formula:
This value of 
corresponds to an angle of 
because 
.
The angle between 
and 
is 
.
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