Basic terms in vectors. Dear friends, here I have explained some basic terms in vectors. These terms are always used in relation to vectors. Have a look!!

### Basic terms in vectors

###### 1) Vector

Vector → Any quantity with magnitude + direction.

Example: velocity

This is because velocity has both speed and direction. Suppose a car is

Suppose a car is moving 80km/hr towards East. After 10 minutes, it’s direction is changed to South from East. But the speed is still the same.

Then, I can say that the car’s velocity is changed since it’s direction is changed.

But its speed has remained the same.

###### 2) Scalar

Scalar → Any quantity with magnitude only.

Example: Speed

This is because it has the magnitude but no direction.

###### 3) Direction of a vector

Suppose any vector is, say, .

This means the direction of the vector is from the vector towards the vector

###### 4) Magnitude of a vector

If is a vector, then its magnitude is written as

###### 5) Standard form of any vector in plane

Standard form of any vector in plane in terms of unit vector is

Its magnitude is

###### 6) Standard form of any vector in space

Standard form of any vector in space in terms of unit vector is

Its magnitude is

###### 7) Direction cosines

Suppose the equation of any vector say, is

By definition, the direction cosines of any vector are the cosines of the angles formed by the vector with and axes.

Thus direction cosines will be

###### 8) Scalar product or dot product of two vectors

If and are two vectors, then

Here is the angle between the two vectors and .

If

then

###### 9) Vector product or cross product of two vectors

If and are two vectors, then

Here is the angle between the two vectors and .

Also is a unit normal vector where form a right-handed set.

If

then

###### 10) Angle between two vectors

If is a vector with direction cosines and is another one with , then the angle between two vectors will be

If the vectors and are perpendicular to each other, then the angle between them is

This means

That makes

###### 11) Unit vectors

- is the unit vector along axis.
- is the unit vector along axis.
- is the unit vector along axis.

###### a. Scalar product of unit vectors

###### b. Vector product of unit vectors

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