gamja
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- 2023
Hi - don't know where to start for i). The solution we were given involved
Thanks in advance for your help!
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Vectors question - 3 vectors and their moduli (1 Viewer)
- Thread starter gamja
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Hi - don't know where to start for i). The solution we were given involved
Thanks in advance for your help!
You can break it down into two steps. Finding a vector in the direction of c and then finding the length of c.
Direction of c: First you're right in that we aren't guaranteed that we have a rhombus. So you make one! If you take the vector a/a, this is unit vector in the direction of a and magnitude 1. Likewise b/b is a unit vector in the direction of b. Since they both have length 1, when you add them, you do form a rhombus. So a/a + b/b has the direction we are looking for because the rhombus means we are bisecting the angle. This means that c = k ( a/a + b/b) for some number k.
Length of c: Length of c is given by sqrt(2ab). Since the length of a/a + b/b is |a/a + b/b|, we first divide by this to make it a unit vector, and then multiply by sqrt(2ab). If you simplify it, you should get something like (ba + ab) / |ba+ab| * sqrt(2ab).
Direction of c: First you're right in that we aren't guaranteed that we have a rhombus. So you make one! If you take the vector a/a, this is unit vector in the direction of a and magnitude 1. Likewise b/b is a unit vector in the direction of b. Since they both have length 1, when you add them, you do form a rhombus. So a/a + b/b has the direction we are looking for because the rhombus means we are bisecting the angle. This means that c = k ( a/a + b/b) for some number k.
Length of c: Length of c is given by sqrt(2ab). Since the length of a/a + b/b is |a/a + b/b|, we first divide by this to make it a unit vector, and then multiply by sqrt(2ab). If you simplify it, you should get something like (ba + ab) / |ba+ab| * sqrt(2ab).
I solved it without using c = sqr(2ab). Where is this question from?View attachment 38425
Hi - don't know where to start for i). The solution we were given involved=k(/a +/b) which contains unit vectors, which I don't really get. I know that we can't just equate k to c, because that would mean that c is a+b which is wrong as question does not imply a rhombus.
Thanks in advance for your help!
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I'm not sure this works because you've assumed that c lies on a straight line between a and b, so you would need to prove this!