Vector A has a magnitude of 19 and is pointing at an angle a=50° east of north.
ID: 1703034 • Letter: V
Question
Vector A has a magnitude of 19 and is pointing at an angle a=50° east of north. Vector B has a magnitude of 26 and is pointing at an angle b=71° 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
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
Given
A = 19 cos50 i + 19 sin50 j
A = 12.2 i + 14.5 j
B = 26 cos 71 (-i) + 26sin 71(-j)
B = -8.46 i - 24.5 j
A + B = (12.2 -8.46)i + (14.5 - 24.5) j
= 3.74 i - 10 j
Magnitude of A +B =(3.74)^2 +(10)^2
A+ B = 10.67
Direction , = tan^-1(-10/3.74) = 69.5^0 along south easten dirrection
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.