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paulb203

Member

Registered: 2023-02-24

Posts: 356

6 feet deep; scalar or vector?

Is 6 feet deep a scalar quantity or a vector quantity?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,654

Re: 6 feet deep; scalar or vector?

6 feet is scalar but deep implies a direction ie downwards so that makes it a vector.

If you were standing in a trench, 6 feet deep, and you fired an arrow upwards you'd have to use the equations of motion to determine what happens next. Those equations use vector quantities, ( except time).

Bob

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paulb203

Member

Registered: 2023-02-24

Posts: 356

Re: 6 feet deep; scalar or vector?

Thanks, Bob.
A student on Khan Academy said it was a scalar, likening it to 6ft tall. That made me think of volume, where the depth would be a scalar, yes? Length, breadth(depth), and height are scalars, yes?
But I also, like you, thought of the deep part as directional, deep translating to down.
But when I thought of down as a direction I thought of south. But when digging down (I thought of a grave) we’re not going south are we, not in the conventional sense at least?
Anyway. I then imagined a treasure map. Walk 30 feet west. Then dig down 6 feet. Could we represent this on an x,y co-ordinate grid, x being east/west, y being up down (I suppose up could apply to the treasure being up a tree, or on a hillside?). What about north/south though? Would we need an x,y,z grid if north/south was also involved?
Nb; Is the ‘down’ in ‘dig down’ superfluous? We can’t dig up! I suppose we could dig at an angle as opposed to straight down, but that would still be down, yeah?
In a nutshell; does it depend on context, whether 6ft deep is a scalar or a vector? If the context is volume, it’s a scalar? If the context is firing arrows upwards from a trench, or digging for treasure, it’s a vector?

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Prioritise. Persevere. No pain, no gain.