Given a is a unit vector, so ∣a∣=1
Also given: (x−a)⋅(x+a)=15
Expanding the dot product:
(x−a)⋅(x+a)
=x⋅x+x⋅a−a⋅x−a⋅a
Since the dot product is commutative, x⋅a=a⋅x, the middle terms cancel:
=x⋅x−a⋅a
=∣x∣2−∣a∣2
Since ∣a∣=1:
∣x∣2−1=15
∣x∣2=16
∣x∣=4
Therefore, ∣x∣=4