The discussion centers on the vector operations involving A = i + j + k and B = -i - j - k, specifically focusing on the calculation of the angle between the resultant vector (A - B) and vector A. Participants clarify that A - B results in 2i + 2j + 2k, and emphasize the importance of using the dot product to determine the angle. The formula used is <A-B><A> = |A-B||A|cos(φ), where φ represents the angle. Misunderstandings regarding vector addition and arithmetic subtraction are addressed, reinforcing the need for proper vector analysis.
PREREQUISITESStudents studying physics or mathematics, particularly those focusing on vector analysis and geometry, as well as educators seeking to clarify vector operations and their implications.
What is 1 - (-1) ?Indranil said:If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
1 - (-1) = 2jbriggs444 said:What is 1 - (-1) ?
Good. So if A = i + j + k and B = -i + -j + -k, what does that make A - B?Indranil said:1 - (-1) = 2
diredragon said:When you figure out where you made a mistake by answering the question jbriggs posted, use the dot product between (A-B) and A to figure out the angle.
##\vec{(A-B)}\vec{A}=|(A-B)||A|\cos\phi##, where ##\phi## is the angle.
If we add A + (-B) = A-B so A + (-B) = i + j + k + (-i + -j + -k) = i + j+ k+ -i +-j + -k = 0jbriggs444 said:Good. So if A = i + j + k and B = -i + -j + -k, what does that make A - B?
You cannot possibly get A -B = 0 unless A = B. Do you have A = B?Indranil said:Homework Statement
If A = i + j + k and B = -i + -j + -k , then (A-B) will make angle with A? What is the concept behind it, could you please explain with a diagram? (this is the part from scalar and vector)
Homework Equations
The Attempt at a Solution
If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
No, I don't A = BRay Vickson said:You cannot possibly get A -B = 0 unless A = B. Do you have A = B?
If B = -i + -j + -k, what is (-B)?Indranil said:If we add A + (-B) = A-B so A + (-B) = i + j + k + (-i + -j + -k) = i + j+ k+ -i +-j + -k = 0
-B = -(-i + -j + -k) = i + j + kjbriggs444 said:If B = -i + -j + -k, what is (-B)?
So work that last bit again. A - B = A + -B. What is A - B?Indranil said:-B = -(-i + -j + -k) = i + j + k
So what to do next?
A + -B = i + j + k + i + j + k = 2i + 2j + 2kjbriggs444 said:So work that last bit again. A - B = A + -B. What is A - B?
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directedicesalmon said:You asked for a geometrical representation; do you understand how to graph a vector? A
Vector is different from a scalar because unlike a scalar, vectors have both a magnitude (length) and a direction (angle). Graphing the point A(1,2) is simple enough, A lies a distance 1 in the positive x direction and 2 in the positive y direction. With the VECTOR <1,2> the values 1, and 2 act as weights on standard unit vectors i = <1,0> and j = <0,1> so A would be the vector sum of 1*<1,0> + 2*<0,1> if you can begin by drawing these two vectors in the x-y plane then you will have a better understanding of what the geometrical representation of a vector is
Do you know how to find the angle between two vectors? What do you know about dot products?Indranil said:then (A-B) will make an angle with A?'
Can you express that answer in terms of A? That should tell you something about the angle between it and A without needing a diagram.Indranil said:A + -B = i + j + k + i + j + k = 2i + 2j + 2k
what to do next?
diredragon said:When you figure out where you made a mistake by answering the question jbriggs posted, use the dot product between (A-B) and A to figure out the angle.
##\vec{(A-B)}\vec{A}=|(A-B)||A|\cos\phi##, where ##\phi## is the angle.
Indranil said:'
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed
Indranil said:'
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed
You need to use vector addition, not arithmetic addition. You need to find the directions of vectors A and B in order to solve the problem. The magnitudes are irrelevant.Indranil said:If we substruct (A-B) we get '0' because 1-1 = 0
Indranil did use vector addition. The error was confusing 1-1 with 1-(-1).David Lewis said:You need to use vector addition, not arithmetic addition. You need to find the directions of vectors A and B in order to solve the problem. The magnitudes are irrelevant.
which is precisely why I asked you to diagram these vectors, presumably you understand basic right angle trigonometry and have been introduced to the notion of a dot product and its relation to the magnitudes of vectors and the angle between them, my post was only meant to help guide you in that direction. Unfortunately nobody here is going to continue to spoon feed you answers, you've got to think about it a bit more here. If you are so lost to the point where you can't even understand why you're lost then you should take a walk and think about that. Return when you at least understand where you're getting confused and we can help guide you a bit more. Good luck!Indranil said:'
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed