Question

can someone explain me what really scalar product of vector means.....

Answer 1

that is fine it is just formula for it......bt y sometimes vector multiplication produces scalar and sometimes vector......

Answer 2

Well it depends which vector multiplication operation it is. Dot/scalar products produce scalar products (durr) whereas cross products yield vector products.

Answer 3

thank u....

Answer 4

Scalar products are a great way to understand how much two vectors are in the same direction.

For example, let i be the unit vector in the x direction. Let v be any vector v = (x,y,z). Then
v.i = x

Answer 5

Now here's something very useful. If
v.i = 0,
then we know that the vector v is perpendicular/at right angles to the x direction.

In other words, v must line in the plane perpendicular to the x-axis.

Answer 6

Very often we use the dot product to establish or find vectors that are perpendicular to each other. For any non-zero vectors v and w, if
v.w = 0
then v and w are perpendicular.

Answer 7

...and also the term "scalar" is opposed to "vector". The scalar product of two vectors gives a plain number without components, not another vector.

Answer 8

Thanks for reply.....i,ve got one more question can vector be represented in 4 dimension space with one time dimension

Answer 9

(x,y,z,t) is a representation of a point in space and time, yes, if that's what you're asking.

Answer 10

In the vector representation (x,y,z,t), time t IS a component of a 4D vector.

This in fact is pretty much exactly how we think about space-time in Einstein's Special Theory of Relativity.

Answer 11

If you want to read a very accessible little book about this, look at this:
http://www.amazon.com/Geometry-Relativity-Fourth-Dimension-Rudolf/dp/0486234002/ref=sr_1_1?ie=UTF8&qid=1324916084&sr=8-1

I found it when I was in 10th grade and loved it for years.

Answer 12

thank you very much.....this means time indeed can be treated as a vector

Answer 13

it's not that time itself is a vector. It's that space-time in Special Relativity can be considered as a 4-dimensional vector space. In that vector space, time is one of the dimensions; space are the other three dimensions.

Answer 14

then y time itself is nt avector

Answer 15

The short answer is time is a scalar quantity: +17, - 5, 0. Asking "why isn't time a vector?" is like asking "Why is the temperature not a vector?" It just isn't necessary to think of it as a vector; thinking of it as a scalar will do.

But for a longer answer about how time is part of a 4-dimensional vector space and interacts with the three normal space dimensions, pick up the book from amazon or your school library and find out.

Answer 16

thanks mr james for time(d) answer