Three vectors 
and 
are such that 
= 
and their magnitudes are in ratio 5 : 4 : 3 respectively. Find angle between vector 
and 
Text Solution
Verified by ExpertsThe correct answer is:
B
Given that : 
= 
+ 
⇒ 
– 
= 
By taking self dot product on both sides 
= 
. 
⇒ A 2 + C 2 – 2 
= 
Now let angle between 
and 
be θ then A 2 + C 2 – 2AC cos θ = B 2
∴ cos θ = 
= 
= 
= 
⇒ θ =cos –1 
= 53º
Or
Since 5 2 = 4 2 + 3 2
The vectors 
and 
make a triangle with angle between 
and 
as 90º.
If θ is the angle between 
and 
, then cos θ = 
= 0.6 = cos (53º)
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