ector A has a magnitude of 30 and is pointing at an angle a=28° east of north. V

Question

ector A has a magnitude of 30 and is pointing at an angle a=28° east of north. Vector B has a magnitude of 34 and is pointing at an angle b=31° south of west. Find the magnitude and direction of A+B (the sum of two vectors is more commonly known as the resultant vector).
Vector diagram
Magnitude of the resultant vector
1
What direction is the resultant vector pointing in?
2
It has no magnitude so the direction is irrelevant. Due east (along the positive x-axis) Due north (along the positive y-axis) Due west (along the negative x-axis) Due south (along the negative y-axis) A northeasterly direction (first quadrant) A northwesterly direction (second quadrant) A southwesterly direction (third quadrant) A southeasterly direction (fourth quadrant)

What is the angle between the resultant vector and the horizontal? If the magnitude of the resultant is zero, then enter 'none'.
3°

Explanation / Answer

Vector A= 30 sin 28 (i) + 30 cos 28 ( j)                = 14.08 i + 26.488 j Vector B = 34 cos 31 ( -i) + 34 sin 31 (-j)                 = -29.14 i - 17.511 j A + B = (14.08 -29.14 ) i +(26.488 - 17.511) j           = -15.06 i + 8.976 j Magnitude of A + B = [(-15.06) 2 + 8.976 2 ]                                = 17.53 Let A+ B makes an angle with west along north then tan = 8.976 / 15.06                                                                                         = 30.79 o Angle with east = 180 -                         = 149.2 o i.e., A northwesterly direction (second quadrant)

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