Question 1204900


magnitude:

{{{abs(a) =sqrt( a[x]^2 + a[y]^2) = sqrt(3^2 + 5^2) = sqrt(9 + 25) = sqrt(34) }}}

direction:

direction defined as the angle theta in standard position of the terminal side through the origin and point with coordinates ({{{a }}}, {{{b}}})
angle theta is found by solving the trigonometric equation:

{{{tan(theta) = b/a}}}, such that {{{0 <= theta < 2pi}}}


Direction {{{theta}}}:  

{{{tan(theta) = 5/3}}}

{{{theta =tan^-1( 5/3)}}}

{{{theta= 59.04}}}° 

The terminal side of vector is in quadrant {{{I}}}.