Vector A has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x-axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, find (a) the vector sum A + B and (b) the vector difference A – B.
Could someone please show me how this problem is done, maybe even with a graph somehow? Thanks
Vectors are directed. When the problem says " is directed along the negative x axis" IT DOES NOT MEAN that. It means the vector is in the same direction as the negative x axis.
Draw from the origin the A vector. At its tip,put a little arrow head. Now, in the DIRECTION of the negative x axis, from the tip of A, draw B.
A+B will then be the vector from the origin to the tip of B.
Now for A-B. From the tip of A, draw B but in the direction of +x axis. From the origin to the tip of that reversed B is A-B.
vecter a has a magnitude of 8.00 uints and makes an angle of 45.0with the positive x-axis?
See
http://i263.photobucket.com/albums/ii157/mathmate/VECTORS.jpg
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Sure! To solve this problem using graphical methods, we can represent the vectors A and B using scaled vector diagrams.
First, draw a coordinate system with the positive x-axis and positive y-axis. Then, draw a vector A starting from the origin and make it 8.00 units long at a 45.0° angle with the positive x-axis. This can be done by drawing a line segment of length 8.00 units making an angle of 45.0° with the positive x-axis. Label the head of this vector as A.
Next, draw a vector B starting from the origin and make it 8.00 units long in the negative x-axis direction. This can be done by drawing a line segment of length 8.00 units in the opposite direction of the positive x-axis. Label the head of this vector as B.
To find the vector sum A + B, we need to add both vectors graphically. To do this, draw a vector C that starts from the tail of vector A (head of vector B) and ends at the head of vector B (tail of vector A). This represents the vector sum A + B. The magnitude of vector C will be the sum of the magnitudes of vectors A and B (8.00 + 8.00 = 16.00 units).
To find the direction of vector C, we can measure the angle it makes with the positive x-axis. Measure the angle between the positive x-axis and the line segment representing vector C. This angle can be measured counterclockwise from the positive x-axis, and it will be the direction of vector C.
For the vector difference A - B, we need to subtract vector B from vector A. This can be done by drawing a vector D that starts from the tail of vector A and ends at the head of vector B in the opposite direction. The magnitude of vector D will be the difference in magnitudes of vectors A and B (8.00 - 8.00 = 0.00 units).
The direction of vector D can be found by measuring the angle it makes with the positive x-axis. Measure the angle between the positive x-axis and the line segment representing vector D. This angle can be measured counterclockwise from the positive x-axis, and it will be the direction of vector D.
That's how you can use graphical methods to find the vector sum A + B and vector difference A - B.