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Tension is definitely a vector as it must point in a direction that opposes the forces creating the tension. Tension is as much a vector as the normal foce is a vector. Don't be a point grubber.

Yes you are correct, Tension is a Scalar Quantity! "When a rope attached to an object is pulling on the object, the rope exerts a force T on the object, and the magnitude T of that force is called the tension in the rope. Because it is the magnitude of a vector quantity, tension is a scalar quantity" (Serway, 2006)

Tension, since it is indeed a force, is a vector; however, the direction is always parallel to the string. Since the string is static, this direction is already given in the problem, and it's therefore redundant to restate the direction. This is why most people only state the magnitude.

Your teacher is pedantic.

You're incorrect, actually. Tension is a scalar quantity since it deals with the internal forces of the rope. At any particular point on the rope you could ask for the tension, and this could be either negative or positive.

Actually Tension is a tensor, not a scalar or vector, and your teacher is sort of correct by saying you need to state the direction of the rope or string because that are always being pulled on never pushed. However, this shouldnt stop you from arguing for your marks. Physics teachers should be pretty lenient if the questions are not specific enough.

It is vectoral in the same sense that velocity is vectoral. A negative force implies a certain direction. Thus, negative tension gives you the following information: the magnitude of the force of tension and the direction in which the force is applied. According to Newton's Third Law, for every action, there is an equal and opposite reaction. This stands true for force of tension. The tension on one particle of the string is matched by an equal and opposite tension by another particle. Generally, this is simplified by indicating two forces on opposite ends of the string applied in opposite directions, but force of tension transmits the force along every single particle of the string.

I think tension is a scalar quantity because it has magnitude but no direction

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Technically, tension is neither a vector nor a scalar. In the case of a rope pulled taught by a force, the tension is constant throughout the string and it behaves much like a scalar. It is actually a two-tensor - give it a direction as input and it tells you the force in that direction, thus the tension seems to have the opposite direction at the two ends of the rope - each end defines a direction (opposite for a rope pulled taught).

Tension is similar to water pressure, which is the same in all directions at a fixed depth. If you give it a direction (a boundary on which it exerts pressure), it produces a force. But like tension, water pressure is itself neither a force nor a vector.

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.