Vector A has a magnitude of 14 and is pointing at an angle a=52° east of north.

Question

Vector A has a magnitude of 14 and is pointing at an angle a=52° east of north. Vector B has a magnitude of 42 and is pointing at an angle b=67° south of west. Find the magnitude and direction of A+B (the sum of two vectors is more commonly known as the resultant vector).

What direction is the resultant vector pointing in? (choose only one)

1. It has no magnitude so the direction is irrelevant.
2.Due east (along the positive x-axis)
3.Due north (along the positive y-axis)
4.Due west (along the negative x-axis)
5.Due south (along the negative y-axis)
6.A northeasterly direction (first quadrant)
7.A northwesterly direction (second quadrant)
8.A southwesterly direction (third quadrant)
9.A southeasterly direction (fourth quadrant)

What is the angle between the resultant vector and the horizontal?

Explanation / Answer

vector A = 14sin(52) i + 14cos(52) j = 11 i + 8.62 j B = -42cos(67) - 42sin(67) = -16.41 i - 38.66 j A+B = -5.41 i -30.04 j magnitude = 30.52 direction = 79.8 degrees below the negative x axis this is in third quadrant southwesterly direction ans : 8 th option

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