Vector v has a magnitude of 23 and a direction angle of 270 degrees. write this vector as a linear combination of the standard unit vectors i and j

For this case we can write the vector in the following way:
 v = 23 (cos (270) i + sin (270) j)
 Rewriting we have:
 v = 23 (0i - 1j)
 v = -23j
 
 The vector written as a linear combination is given by:
 v = -23j