Pre Calculus

Question

Find a unit vector in the same direction as the given vector: v = 3i + 4 j.
a) u=3/25i+4/25j
b) u=3/√7i+4/√7j
c) Vector v = 3i + 4 j is a unit vector.

d) u=3/5i+4/5j

Answer 1

A unit vector u is defined as having its norm llull = 1.

 

A unit vector u_v in the same direction as a given vector v is defined as:

 

u_v = v / llvll

 

with llvll = sqrt( v_i² + v_j² ) : the norm (or magnitude) of vector v

      llvll = sqrt( 9 + 16 ) = sqrt(25) = 5

      llvll ≠ 1 so vector v is not a unit vector

 

so u_v = v/5 = 3/5 i + 4/5 j