What is a unit vector?

If hatn is a unit vector in the direction of the vector vecA , then:-

If hatn is a unit vector in the direction of the vector vecA , them :

If hatn is a unit vector in the direction of the vector vecA , them :

Given that 0.4hati+0.8hatj+b hatk is a unit vector . What is the value of b ?

What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ? What vector should be added to vec a so that the resultant is the unit vector hat i ?

What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ? What vector should be added to vec a so that the resultant is the unit vector hat i ?

What is the unit vector perpendicular to the following vectors 2hati+2hatj-hatk and 6hati-3hatj+2hatk

If P(-1,2) and Q(3,-7) are two points, express the vector PQ in terms of unit vectors hati and hatj also, find distance between point P and Q . What is the unit vector in the direction of PQ ?

What is the unit vector perpendicular to each of the vectors 2hati-hatj+hatk and 3hati+4hatj-hatk ? Prove that the sine of the angle between these two vectors is sqrt(155/156)

If P(-1,2) and Q(3,-7) are two points, express the vectors vec(PQ) in terms of unit vectors hatiand hatj . Also find the distance between points P and Q. What is the unit vector in the direction of vec(PQ) ? Verify that magnitude of unit vector indeed unity.