How Do You Calculate Vector Operations Such as C - A - B and 2A - 3B + 2C?

[kateg4]

If A= 60.0 and theda = 56.5 degrees
of this graph
http://www.flickr.com/photos/44447874@N08/4079278252/

can you help me find C - A - B?
magnitude and direction (counterclockwise from the +x axis is positive)

Also how do I find 2A - 3B + 2C?

Thank you

 

[Andrew Mason]

If A= 60.0 and theda = 56.5 degrees
of this graph
http://www.flickr.com/photos/44447874@N08/4079278252/

can you help me find C - A - B?
magnitude and direction (counterclockwise from the +x axis is positive)

Also how do I find 2A - 3B + 2C?

Thank you

Vector subtraction A = C-B can be remembered this way: Ask yourself: what vector A added to B results in C? This is equivalent to switching the head and tail in B (ie multiplying it by -1) and adding it to C.

C - A - B = C + (-A) + (-B)

To add vectors simply add their respective x components to get the x component of the resultant and add the y components to get the y component of the resultant.

So add the x component of C to -1* the x component of A and add -1* the x component of B. Then to the y component of C add -1* the y component of A + -1* y component of B.

AM

 

[kerimek]

for your question. Subtracting vectors is an important concept in physics and can be represented graphically as well as mathematically. In order to find C - A - B, we can first draw the vectors on the graph provided and label them as A, B, and C. Then, we can use the tail-to-tip method to subtract B from A, which will give us a new vector that we can label as D. This vector D represents the result of subtracting B from A. Next, we can use the same method to subtract C from D, which will give us the final result of C - A - B. We can measure the magnitude and direction of this final vector using a protractor and ruler. The magnitude can be found by measuring the length of the vector and the direction can be found by measuring the angle counterclockwise from the +x axis.

To find 2A - 3B + 2C, we can first calculate 2A and 3B separately using scalar multiplication. Then, we can add these two vectors together using the head-to-tail method to get a new vector E. Finally, we can add 2C to this vector E using the same method to get the final result of 2A - 3B + 2C. Again, we can measure the magnitude and direction of this vector using the same method as before.

In summary, to subtract vectors, we can use the tail-to-tip method and to add vectors, we can use the head-to-tail method. It is important to note that the order in which we subtract or add the vectors can affect the final result, as vector addition is not commutative. I hope this helps in understanding how to find C - A - B and 2A - 3B + 2C.