Finding vectors in Cartesian Coordinates

In summary, to find the vector W such that V + W = -5|V|x, you can use the formula |v| = (vx2 + vy2)1/2 to determine the magnitude of V. Then, to express W in terms of x and y components, you can use the fact that the negative vector has the same magnitude but opposite direction, resulting in the expression w = (-5|V|x) xhat - v. Simplifying this equation gives the final answer of w = (-70.0 xhat + 12.0 yhat) m.
  • #1
uchicago2012
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Homework Statement


The vector V is given by V = (5.0x-12.0y )m. What is W such that V + W = -5|V|x?


Homework Equations


|v| = (vx2 + vy2)1/2


The Attempt at a Solution


I was unsure of what I did to subtract vector v- I know the negative vector has the same magnitude but opposite direction of the positive vector, but I wasn't sure how to express it. I wound up switching the signs to express that they were in different directions.

w = -5 |v| xhat - v
w = (-5)(13 m) xhat + (-5.0 xhat + 12.0 yhat)m
w = (-70.0 xhat + 12.0 yhat) m
 
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  • #2
That looks correct to me.
 

FAQ: Finding vectors in Cartesian Coordinates

What is a vector in Cartesian coordinates?

A vector in Cartesian coordinates is a mathematical representation of a quantity that has both magnitude and direction. It is typically represented by an arrow pointing in a certain direction and its length represents the magnitude.

How do you find the magnitude of a vector in Cartesian coordinates?

To find the magnitude of a vector in Cartesian coordinates, you can use the Pythagorean theorem. This involves taking the square root of the sum of the squares of the vector's components. For example, if a vector is represented as (3, 4), its magnitude would be √(3² + 4²) = √(9 + 16) = √25 = 5.

What is the process for finding the direction of a vector in Cartesian coordinates?

The direction of a vector in Cartesian coordinates can be found by using trigonometric functions. The direction can be represented as an angle from the positive x-axis, and the tangent of this angle is equal to the y-component divided by the x-component of the vector. This angle can then be converted to degrees or radians as needed.

How do I add or subtract vectors in Cartesian coordinates?

To add or subtract vectors in Cartesian coordinates, you can simply add or subtract the corresponding components of the vectors. For example, to add two vectors (2, 3) and (4, 5), you would add the x-components (2+4=6) and the y-components (3+5=8), resulting in a new vector (6, 8).

What is the difference between a scalar and a vector in Cartesian coordinates?

A scalar in Cartesian coordinates is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, speed, and mass, while examples of vectors include velocity, force, and displacement.

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