Define unit vector, null vector and posi-tion vector .

Explanation

Unit vector : A vector whose magnitude is one unit is called unit vector .
Let `bar(a)` is a given vector then unit vector
of = `bar(a)=(bar(a))/(|bar(a)|)=hat(a)`
When `bar(a) ne 0 ` or `(bar(a))/(|bar(a)|)=` unit vector of `bar(a)` . It is denoted by `hat(a)`
Null vector : A vector whose magnitude is zero is called null vector . But it has direction .
for a null vector the origin and terminal point are same .
Ex : Let `bar(A) xx bar(B) = bar(0)` . Here magnitude of `bar(A) xx bar(B) = bar(0)` . But still it has direction perpen-dicular to the plane of `bar(A) and bar(B)` .
Position vector : Any vector in space can be represented by the linear combination of `bar(i) , bar(j)` and `bar(k)` . Let 'O' is the origin then `bar(OP)` is represented as
`bar(OP) = xbar(i) + y bar(j) + z bar(k)` where x , y and z are magnitudes of `bar(OP)` along `bar(i) , bar(j)` and `bar(k)` axis .
Magnitude of ` vec(OP) = sqrt(x^(2) + y^(2) + z^(2))`