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Question

Why is pressure a scalar quantity and stress a vector! Even though both have the same formula !

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Solution

Pressure is a scalar because it is not dependent on direction. In order for a quantity to be considered a vector, it needs to have a magnitude AND a direction. Failing to have the direction part of the vector leaves the quantity as just a magnitude or number or intensity or scalar, whichever word you choose to use.
Pressure becomes similar to a vector when it is multiplied by the differential normal area vector. At that point, it is no longer pressure, but a normal stress vector.
So the only difference between stress and pressure is the multiplication of differential area vector on case of stress. This makes stress as a vector and pressure as a scaler.

Hope it helps.
All the best.

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