f two unit vectors AH and BH are added, the resultant has the magnitude equal to √3. If AH is subtracted from BH, theresultant will have the magnitude

Given that AH and BH are unit vectors, their magnitudes are both 1.

When two vectors are added, the magnitude of the resultant vector is given by the formula:

√[(AH)^2 + (BH)^2 + 2(AH)(BH)cosθ]

where θ is the angle between the two vectors.

Given that the magnitude of the resultant vector when AH and BH are added is √3, we can substitute the known values into the formula:

√3 = √[(1)^2 + (1)^2 + 2(1)(1)cosθ]

Solving this equation gives cosθ = -1/2. This means that the angle between the vectors is 120 degrees (or 2π/3 radians).

When one vector is subtracted from another, the magnitude of the resultant vector is given by the formula:

√[(AH)^2 + (BH)^2 - 2(AH)(BH)cosθ]

Substituting the known values into this formula gives:

Resultant magnitude = √[(1)^2 + (1)^2 - 2(1)(1)(-1/2)]

Solving this equation gives a resultant magnitude of √3.

Therefore, if AH is subtracted from BH, the resultant will have a magnitude of √3.