What is the unit vector in the direction of vector
P=2i+3j-5k.
To find the unit vector in the direction of the vector P given by P = 2i + 3j - 5k, we first need to calculate the magnitude of P and then divide each component of P by its magnitude to get the unit vector.
The magnitude (or length) of P, denoted as ||P||, is given by:
||P|| = √(2^2 + 3^2 + (-5)^2) = √(4 + 9 + 25) = √38
With this magnitude, the unit vector u in the direction of P is obtained by dividing each component of P by ||P||:
u = P/||P|| = (2i/√38) + (3j/√38) - (5k/√38)
To simplify and make it more readable, we can write the unit vector u as:
u = (2/√38)i + (3/√38)j - (5/√38)k
Optionally, you can rationalize the denominators if you prefer:
u = (2√38/38)i + (3√38/38)j - (5√38/38)k
This unit vector u has a length of 1 and points in the same direction as vector P.