Physics Questions: Vectors.?

I would really really apreciate any for someone to help me with these semi-basic vector promblems. I would also appreciate it if you would walk me through the steps as well.





1.)Two Vectors have a magnitude of 5 and 8 that act on a single point cannot have a resultant with a magnitued of....


a. 3 b. 7 c. 13 d. 15





2.) Three forces act concurrently on a n object. The first is a 5 N force actind due east, the second a 3 N force acting due west, and the third is a 4 N force acting due east. Which is the equilibriant force?


a.)12 N, E B.)12 N, W C.) 6 N, W D.)6 N, W








Thank You so much, and I'll help you with your questions! :)

Physics Questions: Vectors.?
1)


the resultant of a and b vector is = sqrt( a^2 + b^2 + 2abcosA)


A is the angle between a and b


now, obviously, the maximum value of cosA is 1.


so the maximum value of the resultant is = sqrt( a^2 + b^2 + 2ab*1) = a + b


so in ur problem, the resultant can't be larger than 5+8 so the answer is d) 15





2) the equillibriant force is a fourth force which is equal and opposite to the resultant of he three mentioned above.


take the east to be +ve and west to be the -ve direction


the resultant of the three forces is = (5 - 3 + 4) N to the east = 6 N force due east


so the equillibriant force is 6 N force to the west

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