Physics Help Forum If A = i + j + k and B = -I + -j + -k, then (A-B) will make angle with A?

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 Jul 16th 2018, 11:16 AM #1 Junior Member   Join Date: Jul 2018 Posts: 14 If A = i + j + k and B = -I + -j + -k, then (A-B) will make angle with A? 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)
 Jul 16th 2018, 12:17 PM #2 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 1,035 I think it's your turn to have a go, right or wrong, before we help you. Note you learn more from getting it wrong than getting it right. If you did this in your opening post you would save lots of time and effort. Hint. Think about what sort of object A, B and (A-B) are. topsquark likes this. Last edited by studiot; Jul 16th 2018 at 12:21 PM.
Jul 16th 2018, 01:15 PM   #3

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 Originally Posted by Indranil 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)
A hint: How do you find the angle between any two vectors?

-Dan
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Jul 16th 2018, 05:48 PM   #4
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 Originally Posted by topsquark A hint: How do you find the angle between any two vectors? -Dan
By dot product of two vectors

Jul 16th 2018, 05:49 PM   #5
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 Originally Posted by studiot I think it's your turn to have a go, right or wrong, before we help you. Note you learn more from getting it wrong than getting it right. If you did this in your opening post you would save lots of time and effort. Hint. Think about what sort of object A, B and (A-B) are.
Would it be unit vectors?

Jul 16th 2018, 06:28 PM   #6

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 Originally Posted by Indranil By dot product of two vectors
So, what is the vector A - B?

-Dan
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Jul 16th 2018, 09:32 PM   #7
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 Originally Posted by topsquark So, what is the vector A - B? -Dan
A-B = A + (-B) = ( i + j + k) + (i + j+ k) = 2i + 2j + 2k

 Jul 17th 2018, 02:54 AM #8 Senior Member   Join Date: Aug 2010 Posts: 403 Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A? topsquark and studiot like this.
Jul 17th 2018, 05:41 AM   #9

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 Originally Posted by HallsofIvy Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?
Good spot. I hadn't noticed that.

-Dan
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Jul 17th 2018, 06:19 AM   #10
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 Originally Posted by HallsofIvy Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?
Indranil
Note that 2 is a scalar. What happens to direction when you multiply (scalar * vector) ?

Note that you asked for diagrams.
I started to think about drawing htese like the last lot but you demonstrated some ability with algebra.

The foregoing discussion shows how much easier algebra is in this 3 dimensional case.

Do you still want diagrams ar can you now draw your own?

One thing you suggested when I asked what A, B and (A-B) are was that they are unit vectors.

Do you still think this or can you see why none of them are unit vectors?

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