Vector manipulations and stuff

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In summary, the conversation involved finding the angle between two position vectors and determining the direction cosines of a vector perpendicular to both. The angle was calculated using two definitions of the dot product and was found to be 153.4°. The perpendicular vector was found using the cross product and had components of (0,0,-5) or (0,0,5). The direction cosines were calculated by dividing each component by the magnitude of the vector and using the perpendicular vector, resulting in direction cosines of 0, 0, and -1. It was confirmed that these answers were correct.
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Homework Statement



Find the angle between the position vectors to the points (3,-4,0) and (-2,1,0) and find the direction cosines of a vector perpendicular to both.

Homework Equations



The Attempt at a Solution



You calculate the angle using the two definitions of the dot product (one that uses the magnitude of the vectors and the other that uses the components of the vectors). The answer is 153.4°. Is it right?

The perpendicular vector is the cross product of the two given vectors (the order of the vectors during the operation is immaterial, right?) and it is (0,0,-5) or (0,0,5). Is that right? The direction cosines are found by dividing the each component by the magnitude of the vector, right? So, using (0,0,-5), we get 0,0 and -1 for the direction cosines. Am I right?

I just need to know that my answers are correct, that's all! Please?
 
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  • #2
Your answers are correct.
 
  • #3
I agree with Kurtz. They are all correct. nice work
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is commonly represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.

2. What are some common operations for manipulating vectors?

Some common operations for manipulating vectors include addition, subtraction, scalar multiplication, dot product, and cross product. These operations allow for the combination, scaling, and comparison of vectors.

3. How are vectors used in physics and engineering?

Vectors are used extensively in physics and engineering to represent physical quantities such as force, velocity, and acceleration. They are also used in geometric and mathematical models to describe the motion and relationships between objects.

4. What are the differences between a vector and a scalar?

A vector has both magnitude and direction, while a scalar only has magnitude. This means that vectors can be added and subtracted, while scalars can only be multiplied or divided.

5. Are vectors only used in two or three dimensions?

No, vectors can be used in any number of dimensions. In fact, they are commonly used in higher dimensions in fields such as computer graphics and quantum mechanics. The principles of vector manipulation remain the same, regardless of the number of dimensions.

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