# Vector with angles with axis (book wrong?)

• kkinsky
In summary: Not quite the "correct" answer but they round to the same numbers.In summary, the question asked for the angles between the vector F and the x, y, and z axes. The correct answer is (107.6, 32.2, 66.2) degrees, which can be found using the direction cosines of the vector. The discrepancy in the "correct" answer of 180 degrees is likely due to a misreading of the question or a mistake in recording the vector's coordinates. It is also helpful to visualize the vector on the three axes to better understand the problem.
kkinsky

## Homework Statement

got a vector F (105,300,140)

magnitude: 347.3

it wants the angles, 3 of them with the axis x y z

why is that?

## The Attempt at a Solution

using AB = |A||b| cos α formula

so with an x-axis the coordinates are (1,0,0)

FX/|F||X|=cos(x-axis angle)

arcos(105/347.3) = x-axis angle

meaning 180-72.4, why am i getting this 180degree descrepency?

try drawing the vector on the three axes and you'll see that your answer reasonable.

Check to see if one of the coordinates have the correct signs in your book like is x=-105?

Your F=(105,300,140) represents a point in the first octant. The angles between the +x, +y, and +z axes must all be less than 90 degrees.However, perhaps you misread the question and missed seeing a minus sign. If your vector F was -(105,300,140), or (-105,300,140), then the correct answer would be 107.6.

By the way, a nice way to do this problem is to use the "direction cosines". If v is a unit vector, $<v_x, v_y, v_z>$, then its components are the cosines of the angles the vector makes with the three axes. That is, if $\theta_x$, $\theta_y$ and $\theta_z$ are the angles the vector makes with the respective axes, then $cos(\theta_x)= v_x$, $cos(\theta_y)= v_y$, and $cos(\theta_z)= v_z$.

Here, F has length $\sqrt{(105)^2+ (300)^2+ (140)^2}= \sqrt{120625}= 347.3$ (approximately). So a unit vector in the direction of F is $<104/347.3, 300/347.3, 140/347.3>= <0.3023, 0.8638, 0.4034>$ so that the angles are $cos^{-1}(0.3023)= 72.4$ degrees, $cos^{-1}(0.8638)= 32.2$ degrees, $cos^{-1}(.4034)= 66.2$ degrees.

## 1. What is a vector with angles with axis?

A vector with angles with axis is a mathematical representation of a physical quantity that has both magnitude and direction. The angles refer to the orientation of the vector with respect to a set of axes.

## 2. How is a vector with angles with axis different from a regular vector?

A regular vector only has magnitude and direction, while a vector with angles with axis also includes information about its orientation with respect to axes.

## 3. Is it possible for a vector with angles with axis to be wrong in a book?

Yes, it is possible for a vector with angles with axis to be incorrectly represented in a book. This could be due to a mistake in calculation or a misinterpretation of the data.

## 4. How can a vector with angles with axis be used in science?

A vector with angles with axis is commonly used in physics and engineering to represent quantities such as velocity, force, and electric field. It allows for a more comprehensive understanding of the physical systems being studied.

## 5. Are there any limitations to using a vector with angles with axis?

One limitation is that the orientation of the axes can vary, leading to different representations of the same vector. Additionally, the use of angles can be more complex and less intuitive than a simple magnitude and direction representation.

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