To find the magnitude of this vector, we will use Pythagorean theorem because this is the shape of a right triangle where the resultant vector corresponds to the hypotenuse.
Magnitude, where we will call 'x' the magnitude or hypotenuse:
(6)^2 + (13)^2 = (x)^2
x^2 = 205 ----------------> now take the square root on both sides
x = root(205) =14.32
magnitude = 14.32
Direction:
to find direction, we will use the formula tanΘ = y/x, where Θ corresponds to the direction of the vector , y is the opposite side and x is the adjacent side.
tan Θ = 13/6 ----------> now take the (tan -1) on both sides to isolate Θ.
tan -1 (tan Θ) = tan -1 (13/6)
Θ = 86 degrees from the horizontal
