SOLUTION: Find the magnitude and direction (in degrees) of the vector. v = 3i +√7j

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Question 539229: Find the magnitude and direction (in degrees) of the vector.
v = 3i +√7j
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If v = ai+bj, then ||v|| = sqrt(a^2+b^2)


In this case, a = 3 and b = sqrt(7)


||v|| = sqrt(a^2+b^2)


||v|| = sqrt(3^2+(sqrt(7))^2)


||v|| = sqrt(9+7)


||v|| = sqrt(16)


||v|| = 4


So the magnitude of v is 4


To find the direction or angle, we use the idea that theta = arctan(b/a)


theta = arctan(b/a)


theta = arctan(sqrt(7)/3)


theta = 41.409622 (note: this is approximate)


So the direction is roughly 41.409622 degrees.