Find a unit vector in the direction of vector PQ , where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively. ​

Question

Find a unit vector in the direction of \(\vec {PQ}\) , where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively.

Answer 1

We have,

Coordinates of P is (5, 0, 8).

Coordinates of Q is (3, 3, 2).

So,

Position vector of P is given by,

To find unit vector in the direction of PQ, we need to find position vector of PQ.

Position vector of PQ is given by,

We know that, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector.

For finding unit vector, we have the formula:

Thus, unit vector in the direction of PQ is