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Question

Let ^a and ^b be two unit vectors. If the vectors c=^a+2^b and d=5^a4^b are perpendicular to each other, then the angle between ^a and ^b is

A
π6
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B
π2
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C
π3
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D
π4
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Solution

The correct option is D π3
Given that c and d are Perpendicular
c.d=0
Putting values
5|a|2+6ab8|b|2=0
6a.b=3
a.b=12
=|a||b|cosθ=12
Since a and b are Unit vectors
So, cosθ=12
θ=π3
Hence, option 'C is correct.

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