(x+y)a cap + (x-y)b cap = root[2(x^2 +y^2)] then what is the angle between a cap and b cap
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As the two vectors are perpendicular,
Their dot product is zero
(a+2b)(5a-4b)=0
5a^2+6abcos(theta)-8b^2=0 (costheta is angle between acap and bcap)
As you mentioned acap and bcap, it means that they are unit vectors and have magnitude 1.
5+6costheta-8=0
Costheta=3/6=1/2
Theta=pi/3 or 60 degrees
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