Solving components of vectors

In summary, to find the resultant vector C, we need to add the i hat components of A and B, as well as the j hat and k hat components of B. Since the resultant vector is zero, all of these components must sum to zero. Using the tail to head rule, we can connect the vectors and solve for the components of C.
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Homework Statement


Let resultant vector A = 17 i hat - 42 j hat and resultant vector B = 31 j hat + 18 k hat. Find the resultant vector C such that the sum of resultant vector A, B and C equals resultant vector zero. Find the i,j and k components of resultant vector C.

Homework Equations


understand the basic of vectors i hat is in the x-axis and j hat is the y axis. negative vector points down and left. positive vectors point right and up. use the tail to head rule to connect vectors.


The Attempt at a Solution


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I'm not sure how to go about solving this problem. Do I add the vectors with the same hats?
 
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  • #2
Yes. If a resultant vector is 0, then it can't have any components. So when you add up the individual vectors with the same hats , they must sum to___??____. Watch plus and minus signs.
 

1. What are the components of a vector?

The components of a vector are the vertical and horizontal parts that make up the vector's magnitude and direction.

2. How do you solve for the components of a vector?

To solve for the components of a vector, you can use trigonometric functions such as sine and cosine. The vertical component can be found by multiplying the magnitude of the vector by the sine of the angle between the vector and the vertical axis. Similarly, the horizontal component can be found by multiplying the magnitude of the vector by the cosine of the angle.

3. Why is it important to solve for the components of a vector?

Solving for the components of a vector allows us to understand the direction and magnitude of the vector, which is essential in many scientific and mathematical applications. It also makes it easier to perform calculations and make predictions based on the vector's properties.

4. Can you solve for the components of a vector without knowing its magnitude?

No, it is not possible to solve for the components of a vector without knowing its magnitude. The magnitude is a crucial factor in determining the components, as it is used in the equations for finding the vertical and horizontal components.

5. How can solving for the components of a vector be applied in real life?

Solving for the components of a vector can be applied in various real-life scenarios, such as in navigation and engineering. It can also be used in physics to analyze the motion of objects and understand the forces acting on them. Additionally, it can be helpful in computer graphics to determine the direction and intensity of visual effects.

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