Vector A has a magnitude of 11 and is pointing at an angle a=34° east of north.
ID: 2047624 • Letter: V
Question
Vector A has a magnitude of 11 and is pointing at an angle a=34° east of north. Vector B has a magnitude of 22 and is pointing at an angle b=28° south of west. Find the magnitude and direction of A+B (the sum of two vectors is more commonly known as the resultant vector).Magnitude of the resultant vector
1
What direction is the resultant vector pointing in?
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'
Explanation / Answer
A=11 (cos(34)i +sin(34)j)=9.11 i + 6.15 j B= 22(-cos(28)i - sin(28)j)=-19.42 i - 10.32 j A+B=-10.31 i -4.17 j magnitude of A+B = sqrt(10.31^2+ 4.17^2)=11.12 direction= tan^-1(4.17/10.31)=86.33 degrees the x,y components of A+B are negative... third quadrant (south westerly) angle with horizantal= 86.33 degrees with west direciton I took the magnitude of B wrong the first time..
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