Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 337

Scalars and Vectors

When it comes to velocity, for example, why might someone want to know both the speed and direction of an object?

If someone was caught speeding the relevant information would be their speed, a scalar quantity; their direction would be irrelevant.

Why might someone want to know their speed AND direction (other than a physics teacher asking a student a hypothetical question for the purpose of learning)?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,636

Re: Scalars and Vectors

I can see there's a lion approaching.  Would you just like to run in a random direction or would it be helpful to know which direction is best?

My ship is wanting to intercept another ship on the ocean. It is also moving.  How do I plot a course so that we meet at some place ahead? Shall I just choose a new speed or might it also be useful to consider the direction of travel?

Three ropes are tied together in a knot.  Two others are ready to pull on their ropes and want me to pull also so that, together,  our forces exactly balance.  Do you think it matters which directions we each choose for our pull?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 337

Re: Scalars and Vectors

Thanks, Bob.
All obvious, doh!
I think the new terms had me overthinking it. Vectors. Scalars. Sounded complicated. And velocity, which I’d always thought of as a fancy word for speed, not being quite the same as speed.
Your lion example reminded me of the old one; Two guys on safari spot a lion. One takes his Nike Sprints out of his backpack, starts putting them on. The other says, “You’ll never outrun a lion.” The first says, “No, but I’ll outrun you.”

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Prioritise. Persevere. No pain, no gain.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 255

Re: Scalars and Vectors

A vector can be seen, for example, as 2 scalars (in a 2D space, as a scalar on the X axis and another on the Y axis) or 3 scalars (in 3D space, on X, Y and Z) which defined it.
In 2D space, adding two vectors is simply adding their 2 scalars on X also their two scalers on Y. These two sums define the resultant vector.

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

paulb203

Member

Registered: 2023-02-24

Posts: 337

Re: Scalars and Vectors

Thanks, KerimF

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Prioritise. Persevere. No pain, no gain.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 255

Re: Scalars and Vectors

I thought that scalar could be an algebraic number that is positive or negative. It seems it has to be, by definition, a positive number only (including 0).
In this respect, I am afraid that my post #4 is wrong. What I called scalar on the X, Y or Z axis is also a vector but in a 1D space. Sorry for this mistake.

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

paulb203

Member

Registered: 2023-02-24

Posts: 337

Re: Scalars and Vectors

Thanks, KerimF

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,636

Re: Scalars and Vectors

Not all authorities agree that a scalar must be positive.

Eg. Temperature is a scalar and on some scales can  be negative.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob