# Two questions about vectors and scalars?

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• Feb 24th 2011, 04:11 PM
Barthayn
Two questions about vectors and scalars?
Is vector A divided by magnitude of a, is a scalar or a vector. I think it is a vector because the direction is not eliminated.

My other question is, using vectors explain why |a+b| is always less than |a|+|b|.
I think it is always smaller than |a|+|b| because it goes in a straight line, from point a to point c, and not a-to-b-to-c. For example, |a+b| of the 3,4,5 triangle is 5, while |a|+|b| is 7. This means you will have a less magnitude because you will be going in a straight line.
• Feb 25th 2011, 01:09 AM
emakarov
Quote:

Originally Posted by Barthayn
Is vector A divided by magnitude of a, is a scalar or a vector. I think it is a vector because the direction is not eliminated.

Yes. (Is it significant that you used an uppercase and a lowercase a?) The magnitude of a vector is a scalar, and a vector multiplied or divided by a scalar is a vector.

Quote:

My other question is, using vectors explain why |a+b| is always less than |a|+|b|.
I think it is always smaller than |a|+|b| because it goes in a straight line, from point a to point c, and not a-to-b-to-c. For example, |a+b| of the 3,4,5 triangle is 5, while |a|+|b| is 7. This means you will have a less magnitude because you will be going in a straight line.
This is called the triangle inequality.
• Feb 25th 2011, 05:01 AM
Soroban
Hello, Barthayn!

Quote:

$\text{Is vector }\vec a\text{ divided by magnitude of }\vec a\text{ a scalar or a vector?}$

$\text{I think it is a vector because the direction is not eliminated.}$

You are correct!

In fact, this has a special name.

. . $\dfrac{\vec v}{|\vec v|}\,\text{ is the }unit\:vector\text{ in the direction of }\vec v.$