Numerical problem on vector algebra - components of vectors

In summary, the question asks for the magnitude and direction of the second run of Beetle 2 in order to end up at the same location as Beetle 1, which has made two runs of 0.50m due east and 0.80m at 30° north of due east. Beetle 2 has already made a run of 1.6m at 40° east of due north. This problem is from Fundamentals of Physics by Resnick/Halliday and a diagram may be helpful in solving it.
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Homework Statement



Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50m due east, then 0.80m at 30° north of due east. Beetle 2 also makes two runs; the first is 1.6m at 40° east of due north. What must be (a) the magnitude and (b) the direction of its second run if it is to end up at the new location of beetle 1?

This is a question from Fundamentals of Physics by Resnick/Halliday. Can someone solve it and if possible attach a diagram? Thanks in advance to anyone who solves it or atleast gives it a try. :^:
 
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You need to first make an attempt at a solution. At least let us know what is giving you a fit, and we can then help.
 

1. What is a vector in algebra?

A vector in algebra is a mathematical quantity that has both magnitude (size) and direction. It is represented by an arrow and can be used to represent physical quantities such as velocity, acceleration, and force.

2. What are the components of a vector?

The components of a vector are the parts of the vector that are parallel to the axes of a coordinate system. In two-dimensional space, a vector has two components: one in the horizontal direction (x-axis) and one in the vertical direction (y-axis). In three-dimensional space, a vector has three components: one in the x-direction, one in the y-direction, and one in the z-direction.

3. How do you find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem. This involves taking the square root of the sum of the squares of the vector's components. For example, in two-dimensional space, the magnitude of a vector v is given by √(vx² + vy²).

4. How do you find the direction of a vector?

The direction of a vector can be found by using inverse trigonometric functions. In two-dimensional space, the direction of a vector v can be found by taking the inverse tangent of the y-component divided by the x-component (arctan (vy/vx)). In three-dimensional space, the direction of a vector can be found using spherical coordinates.

5. How do you add or subtract vectors?

To add or subtract vectors, you must add or subtract their corresponding components. For example, to add two vectors v1 and v2 in two-dimensional space, you would add their x-components and their y-components separately: v1 + v2 = (v1x + v2x)i + (v1y + v2y)j. The same process applies for subtraction, but with the components being subtracted instead of added.

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