Kinematics question -- Adding and subtracting vectors

[chardy87]

Homework Statement

If vector
a

is added to vector
b

,
the result is the vector
c

= (7.00, 3.00).
If
b

is subtracted from
a

,
the result is the vector
d

= (−4.50, 9.25).

what is the magnitude of a?
what is the magnitude of b?

Homework Equations

The Attempt at a Solution

a + b = (7.00, 3.00)c
a-b=(-4.50,9.25)d
2a=(c + d)
(c+d/2) = a
a=(1.25,6.13)

b =c-a
b=(5.75,-3.13)

 

[berkeman]

(c+d/2) = a
a=(1.25,6.13)

b =c-a
b=(5.75,-3.13)

Looks mostly right, but your parenthesis is misplaced slightly in the first quoted equation above. It should be (c+d)/2 = a

But you still did the math right, it's just a typo in how you wrote the equation. Also, Does your instructor want you to round to 6.13 and -3.13, instead of 6.125 and -3.125?

 

[chardy87]

The answer is supposed to be one number (2.00 for example). I'm unsure how to get this as I have coordinates.

 

[berkeman]

The answer is supposed to be one number (2.00 for example). I'm unsure how to get this as I have coordinates.

Oh, I see now. They are asking for the "magnitude" of each vector, not the components of the vector. Do you know how to get the magnitude and direction of a vector in polar coordinates given the components in rectangular coordinates?

Hint -- do not round your answers until the very last step.

 

[chardy87]

No I do not know how to do that.

 

[berkeman]

No I do not know how to do that.

It should be in your textbook or the study materials for this problem set.

Alternately, go to Google and search on rectangular to polar conversion.

 

[Ray Vickson]

No I do not know how to do that.

You do not need to go to polar coordinates. Just Google "magnitude of vector".

Basically, a (2-dimensional) vector (a,b) is a point in the Cartesian plane, with x-coordinate 'a' and y-coordinate 'b'. The magnitude of (a,b) is just the distance from the point (a,b) to the origin (0,0).