Find Vector Components: A (17, 27°), B (26, 75°)

In summary: This will give you the components of C. In summary, the components of vector C for the given operations are: (a) C = A + B (39, 56) (b) C = A - B (-7, -25) (c) C = A + 4B (102, 139) (d) C = -A - 7B (-168, -237)
  • #1
susyq232
2
0
Vector A has a magnitude of 17 (in some unspecified units) and makes an angle of 27° with the x axis, and a vector B has a length of 26 and makes an angle of 75° with the x axis. Find the components of the vector in the following.
(a) C = A + B
( , )

(b) C = A - B
( , )

(c) C = A + 4B
( , )

(d) C= -A-7B
( , )




I did the entire problem and submitted it to webassign and it came back as wrong.

what i first did was draw vector a from the origin pointing up diagnally between the x and y axis. then from the tip of that i connected the tail of b pointing in also up diagnally between the x and y just with a sharper angle ( so the a is shaped like the bottwem half of the symbol '>' and then i added a '/' symbol to the tip)

so that's my picture. then i connected the end of A and the tip of B with a vector C. i then solved all the lengths of the smaller triangles then added ax and bx and ay and by to get the entire c vector's triangle for a+b = c. then i did ax-bx and ay-by to fnd a-b=c and so on.



my answers i got for the problem that webassign says is wrong:
(a) c= a + b
(39,56)

(b) c= a-b
(-7,-25)

(c) c= a + b4
(102,139)

(d) c= -a -7b
(-168,-237)
 
Last edited:
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  • #2
did you make any attempt at the problem? If you arent sure where to start, break the vectors A and B into their x and y components
 
  • #3


I would suggest double checking the calculations and making sure that the units are consistent throughout the problem. It is also important to carefully label the components of the vectors and make sure they are added/subtracted correctly. If the answers still do not match with the answer key, it may be helpful to seek assistance from a teacher or tutor to review the problem and identify any errors. Additionally, it may be helpful to practice more problems involving vector components to improve understanding and accuracy.
 

Related to Find Vector Components: A (17, 27°), B (26, 75°)

1. What is the magnitude of vector A?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude (or length) of a vector is equal to the square root of the sum of the squares of its components. In this case, the magnitude of vector A is equal to √(17² + 26²) = 31.8 units.

2. How do I find the x and y components of vector B?

To find the x and y components of a vector, we use trigonometric functions. The x component (or horizontal component) of vector B can be found by multiplying the magnitude of B by the cosine of its angle, which is 26 * cos(75°) = 6.3 units. Similarly, the y component (or vertical component) of B can be found by multiplying the magnitude of B by the sine of its angle, which is 26 * sin(75°) = 25.1 units.

3. What is the direction of vector A?

The direction of a vector is given by its angle with respect to the positive x-axis. In this case, vector A has an angle of 27° with respect to the positive x-axis in the counterclockwise direction.

4. Can I use these vector components to find the resultant vector of A and B?

Yes, the resultant vector of A and B can be found by adding their respective x and y components. In this case, the resultant vector would be R = (17+6.3, 25.1+25) = (23.3, 50.1).

5. How do I represent these vector components graphically?

Vector components can be represented graphically using a coordinate plane. The x component is represented by a horizontal arrow and the y component is represented by a vertical arrow, both starting from the origin. In this case, vector A would be represented by an arrow with a length of 17 units at an angle of 27° from the positive x-axis, and vector B would be represented by an arrow with a length of 26 units at an angle of 75° from the positive x-axis.

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