Anonymous
Anonymous asked in Science & MathematicsPhysics · 9 years ago

# Vector quantity question: What is unit vector?

Please explain what is this UNIT VECTOR , what is its use, how it is used and what is î, ĵ, k^?

I know the definition already: "It is the vector whose magnitude is 1" but I didn't understand what it means, how can you say that the magnitude of every unit vector is 1??

Isn't it written as A = 3î +6ĵ+ 4k^? then how is its value 1?

I am confused, so long explanations are better.

Relevance
• 9 years ago

As you know the definition of unit vector , i Shall try and explain unit vector in a very informal way so that u can try and understand the concept of it:

just giving you a simple ex: suppose you go to a shop and buy a 5kg vegetables there it is 5 times 1kg of the vegetable you are buying so here u could consider 1kg as similar to 1 vector but 1kg is a scalar and hence has only magnitude but no direction....but vector has both magnitude and direction....

so when you write A=3i+6j+4k (i suppose you know that i is the unit vector in x direction and j is the unit vector in y direction and k is the unit vector in the z direction)...hence it 3 times unit vector in x direction , 6 times the unit vector in y direction and 4 times the unit vector in z direction. finally A gives us the resultant vector.

• 9 years ago

Vectors are a geometric way of representing quantities that have direction as well as magnitude. An example of a vector is force. If we are to fully describe a force on an object we need to specify not only how much force is applied, but also in which direction. Another example of a vector quantity is velocity -- an object that is traveling at ten meters per second to the east has a different velocity than an object that is traveling ten meters per second to the west. This vector is a special case, however,sometimes people are interested in only the magnitude of the velocity of an object. This quantity, a scalar, is called speed which has magnitude but no given direction.

When vectors are written, they are represented by a single letter in bold type or with an arrow above the letter, such as or . Some examples of vectors are displacement (e.g. 120 cm at 30°) and velocity (e.g. 12 meters per second north). The only basic SI unit that is a vector is the meter. All others are scalars. Derived quantities can be vector or scalar, but every vector quantity must involve meters in its definition and unit.

• Anonymous
9 years ago

A UNIT VECTOR is by definition a vector of Magnitude "one" (1) and no units of measurement associated to it.

If Á is a vector and A its magnitude, then the unit vector Â - pointing in the direction of Á - is given by:

Â=Á/A

They are useful when you need to give a scalar quantity a certain direction, but don't wish to change its value.

Unit vectors have magnitude 1 by definition but they can compose other vectors through vector algebra (head-to-tail summing). If you define vector Á

Á = 3î +6ĵ+ 4k^

Its magnitude is not one as A=sqrt(3²+6²+4²) and by definition it is not a unit vector.

What really are the unit vectors are the individual components i, j and k, which are scaled by 3, 6 and 4 respectively, giving the Á vector it's magnitude and direction.

The unit vectors i j and k point respectively towards the positive x, y and z directions and have magnitude 1. You can make a unit vector point in any direction though, using the formula I first stated.

You can easily identify unit vectors by the ^ (hat) notation.

Cheers!

Source(s): Math Minor with Vector calculus
• 4 years ago

RE:

Vector quantity question: What is unit vector?

Please explain what is this UNIT VECTOR , what is its use, how it is used and what is î, ĵ, k^?

I know the definition already: &quot;It is the vector whose magnitude is 1&quot; but I didn&#39;t understand what it means, how can you say that the magnitude of every unit vector is 1??

Isn&#39;t it...

Source(s): vector quantity question unit vector: https://shortly.im/D9HOZ
• 9 years ago

Actually a short answer is much better, since its so simple really.

Notice the word ... "Unit"

This word MEANS .. "single" ... or "one"

So when you say "unit vector" , it MEANS "vector of size one".

Only the DIRECTION is left unspecified.

So in your example, i j & k each have size 1, but their directions are whatever is specified for them.