you have two position vectors that need to be combined in different ways. The fi

Question

you have two position vectors that need to be combined in different ways. The first vector is: A(arrow) = 2.0i^ -5.0j^. The second vector is: B(arrow) =2.0i^ + 2.0j^. Assume that all values are given in meters.

What are  (a) magnitude and (b) direction (angle relative to the x-axis) of A?

Also, what are the (c) magnitude and (d) direction (angle relative to the x-axis) of B?

Also, what are the (e) magnitude and (f) direction (angle relative to the x-axis) of A(arrow) +B(arrow)?

Finally, what are the (g) magnitude and (h) direction (angle relative to the x-axis) of 2A(arrow) -3B(arrow)?

Please show work step by step for each part so I can understand how to do the problem. Thanks!

Explanation / Answer

A = 2i - 5j

B = 2i + 2j

a) magnitude of A = sqrt(2^2 + 5^5) = 5.385

b) arctan(-5/2) = 360-68.19 = 291.81 deg

c) |B| = sqrt(2^2 + 2^2) = 2.828

d) arctan(2/2) = 45 deg

e) A+B = 4 i - 3j

|A+B| = sqrt(25) = 5

f) arctan(-3/4) = 360 - 36.86 = 323.14 deg

g) 2A - 3B = (4-6) i + (-10-6)j = -2i-16j

|2A-3B| = sqrt(2^2 + 16^2) = 16.124

h) arctan(-16/-2) = 262.87 deg

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