SOLUTION: Given that A=< 3,1 > and B= <-2,3>, find the magnitude and direction angle for each of the following vectors. Give exact answers using radicals when possible, otherwise round to th

Algebra ->  Trigonometry-basics -> SOLUTION: Given that A=< 3,1 > and B= <-2,3>, find the magnitude and direction angle for each of the following vectors. Give exact answers using radicals when possible, otherwise round to th      Log On


   

Question 925093: Given that A=< 3,1 > and B= <-2,3>, find the magnitude and direction angle for each of the following vectors. Give exact answers using radicals when possible, otherwise round to the nearest tenth.
1.) A+B:
2.) 1/2A-2B:
3.) -3A:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) (3,1)+(-2,3)=(3-2,1+3)=(1,4)
Mag:sqrt%281%5E2%2B4%5E2%29=sqrt%2817%29
Direction: tan%28theta%29=4%2F1
theta=76degrees
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2) (0.5)(3,1)-2(-2,3)=(3/2+4,1/2-6)=(11/2,-11/2)
Mag:sqrt%28%2811%2F2%29%5E2%2B%2811%2F2%29%5E2%29=%2811%2F2%29sqrt%282%29
Direction: tan%28theta%29=-1
theta=335degrees
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3) 3(3,1)=(9,3)
Mag:sqrt%28%289%29%5E2%2B%283%29%5E2%29=sqrt%2890%29=3sqrt%2810%29
Direction: tan%28theta%29=3%2F9
theta=18.4degrees
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