Find the magnitude and direction angle of v=8 (cos135i+sin135j)

The magnitude of the vector will be given by:

v = root ((8cos135) ^ 2 + (8sin135) ^ 2)

v = root ((8) ^ 2 * ((cos135) ^ 2 + (sin135) ^ 2))

v = root ((8) ^ 2 * (1))

v = root ((8) ^ 2)

v = 8

The angle is:

theta = Atan ((8sin135) / (8cos135))

theta = Atan (tan135)

theta = tan135

Answer:

The magnitude and direction angle are:

v = 8

theta = tan135