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) (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.
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