Basic Calculus help with finding components

In summary, the conversation discusses finding a place for homework help and registering on the site. The given problem involves finding the displacement and angle between three displacements and the components of d1 along the direction of d2 and perpendicular to d2. The solutions for the components and angle are given and the confusion is clarified by using the Pythagorean theorem.
  • #1
Zyxer22
16
0
I always seem to find this place whenever I'm in need of homework help, so I finally decided to register (and hopefully post in the right area).

My given problem is


Here are three displacements, each in meters: d1 = 4.2i + 2.7j - 7.9k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j + 2.0k. What is r = d1 - d2 + d3 ((a), (b) and (c) for i, j and k components respectively)? (d) What is the angle between r and the positive z axis? (e) What is the component of d1 along the direction of d2? (f) What is the component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2?

The solutions I've gotten are

a) 9.2 m
b) 3.7 m
c) -8.9 m
d) 131.91°
e) -6.01 m
f) 7.16 m

All of which I know to be correct. The confusion I'm having is with part f. I used this equation to solve for f:

[(magnitude of d1)^2 - (the component of d1 along the direction of d2)^2]^1/2

I just don't understand why this works. Anyone help?
 
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  • #2
This follows the pythagorian theorem. If you draw it to yourself, you'll see the the projection of d1 on d2, and d1 itself, form to vectors, which by connecting their ends form a right triangle. This is generally true for all vectors.
 
  • #3
I appreciate the answer. And, actually, now that I see it, this should've been really obvious. Thank you ^^
 

1. What is calculus?

Calculus is a branch of mathematics that deals with the study of change and motion. It involves the use of mathematical methods and concepts to analyze and solve problems related to rates of change, accumulation, and optimization.

2. What are the two main branches of calculus?

The two main branches of calculus are differential calculus and integral calculus. Differential calculus focuses on the study of rates of change, while integral calculus deals with the accumulation of quantities.

3. What are the basic components of calculus?

The basic components of calculus are functions, limits, derivatives, and integrals. Functions are mathematical relationships between two quantities, limits describe the behavior of a function as the input approaches a certain value, derivatives measure the instantaneous rate of change of a function, and integrals calculate the total accumulation of a function over an interval.

4. How do I find the components of a function?

To find the components of a function, you will need to understand the function's definition, domain and range, and any special characteristics such as symmetry or asymptotes. You can also use mathematical techniques such as differentiation and integration to find the derivatives and integrals of the function.

5. Why is calculus important?

Calculus is important because it provides a powerful set of tools for solving real-world problems in fields such as physics, engineering, economics, and statistics. It also helps to develop critical thinking and problem-solving skills that are applicable in various areas of life.

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