# Definition clarification of vector mag/direction/rant

• GreenLantern
In summary, the conversation revolves around a student's concern about receiving a lower grade on a physics test due to a misunderstanding of the definition of magnitude and direction of a vector. The conversation also touches upon the importance of units and significant figures in answering questions accurately. Despite some disagreement, the general consensus is that the student's answer did not fully meet the criteria for the question and it would be unlikely for the grade to be changed.
GreenLantern
Okay so I feel this is a bit of a weak first post in a forum but I haven't yet found a place for comment that wouldn't just be useless clutter in the forum.

So I am currently a second semester Mechanical Engineering student and have been getting A's on every test in every class this semester...until now. I took my third to last physics test on friday and received it back on monday with a 76%. As i started to look through the test I saw that I lost 12 points (total from two separate problems) because of one simple thing.

On two questions he asks for a vectors magnitude and direction. Now the way I've always considered this was it could be answered in two forms. A resultant vector magnitude and a direction given in terms of an angle or unit vector OR it could be given in terms of vector components. At least this has been gravy for my calc/engineering classes...

What do you all think?
is:
$$\vec{F}$$=[5$$\hat{j}$$ + 3$$\hat{k}$$]​

considered magnitude and direction of a vector?

heres one of the actual problems (at the beginning of the test he specifically mentioned vector as the answer for it)

sorry its so massive...but am I really wrong in this? I got the correct components but is this really considered as not an accurate answer for the magnitude and direction of the magnetic field warranting a loss of 7/20 points? And should I even care enough to try and get it changed because this is the third out of three tests with which the one with the lowest grade gets dropped (this test score wouldn't count no matter wether i received the 12 points or not)

thanks everyone (hope this is the right forum)

-GreenLantern

No, you shouldn't care to try and get another grade, because you won't get it.

The magnitude of a vector is a scalar quantity, you have not identified it.

Whether you had given the "direction" in terms of a UNIT vector, or as an angle it makes with, say, the positive x-axis is of less relevance.

You have shown a proficiency at basic math calculations (hence more than 50% correct), but you betray a hazy understanding of standard definitions of terms.

I fully agree with giving you just 65% correct on that question.

GreenLantern said:
What do you all think?
is:
$$\vec{F}$$=[5$$\hat{j}$$ + 3$$\hat{k}$$]​

considered magnitude and direction of a vector?
Absolutely not. The magnitude of the vector you wrote above $$\sqrt{5^2+3^2}\approx 5.83$$.

The question very specifically asked for the magnitude and direction of the total magnetic field at the origin. You didn't answer the question.

I see why the OP feels harsh, since in some form the OP has indeed given the precise "magnitude and direction" (as opposed to just the strength, or just the general direction).

But if I were marking the exam question, I wouldn't give full marks unless it clearly terminated in a plain English sentence that not only answers but re-acknowledges all parts of the original question (and suggests a full conceptual understanding): "The total magnetic field at the origin has magnitude ... and direction ...", with the correct number of significant figures (if not a full uncertainty analysis) and correct units.

The OP had completely neglected units of measurement (a number is meaningless on its own), used an inappropriate number of significant figures (showing a lack of respect for uncertainty, one of the most important facets of measurement), and worst of all, expressed an answer using undefined symbols (who knows how you expect j,k to be interpreted, why not at least use the same symbols as provided?). In the real word, such a response would be completely useless, since a person who did not already know how to themselves answer the question they asked, would still not be able to properly interpret all of it from your response.

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## 1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction of the vector.

## 2. What is vector magnitude?

Vector magnitude is the size or length of a vector. It is a scalar quantity, meaning it only has a numerical value and no direction.

## 3. How is vector magnitude calculated?

The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of its components. In other words, if a vector is represented by the components x and y, its magnitude is given by √(x² + y²).

## 4. What is vector direction?

Vector direction is the orientation of a vector in space, usually measured in degrees or radians. It is often represented by a unit vector, which is a vector with a magnitude of 1 that points in the same direction as the original vector.

## 5. How is vector direction represented?

Vector direction is typically represented using angles or coordinates. In a 2D coordinate system, the direction of a vector can be described using the angle it makes with the positive x-axis. In a 3D coordinate system, the direction can be described using spherical coordinates or unit vectors in the x, y, and z directions.

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