Can you show me how to get each of these answers?? Given two vectors a = 3.31 -3

Question

Can you show me how to get each of these answers??

Given two vectors a = 3.31 -3.4j and b =6.3i + 8.4j what is the magnitude (in m) of the vector a? Find the direction (in degree = deg) of the vector a. Find the magnitude of the vector b. Find the direction (in degree) of the vector b. Find the magnitude of the vector a + b. Find the direction of the vector a + b. Find the magnitude of the vector b-a. Find the direction of the vector b-a Find the magnitude of the vector a-b. Find the direction of the vector a-b

Explanation / Answer

magnitude of a = sqrt (3.32 + 3.42) = 4.738 m

direction of a = arctan(-3.4/3.3) = -45.855 = 314.140 = 3.14*102 deg

magnitude of b = sqrt (6.32 + 8.42) = 10.5 m

direction of b = arctan(8.4/6.3) = 53.13 deg = 5.31*10 deg

a+b = 9.6i + 5j

magnitude of a+b = sqrt (9.62 + 52) = 10.824 m

direction of a+b = arctan(5/9.6) = 27.51 deg

a-b = -3i -11.8j

magnitude of a-b = sqrt (32 + 11.82) = 12.175 m

direction of a-b = arctan(11.8/3) = 75.73 deg

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