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Vector Algebra

A, B and C are three points with coordinates (4, 0, 8), (2, 6,10) and (0,1,1) (in meters) respectively. Two forces act through A, one of 13.266 kN in the direction AB and a second given (in units of kN) by the vector (8, 1, 2).Calculate: a)The resultant force through A
b)The resultant force through A in the direction of the vector (1, 2, 2).
c)The moment due to each force about the point C.
Original post by chidzix
A, B and C are three points with coordinates (4, 0, 8), (2, 6,10) and (0,1,1) (in meters) respectively. Two forces act through A, one of 13.266 kN in the direction AB and a second given (in units of kN) by the vector (8, 1, 2).Calculate: a)The resultant force through A
b)The resultant force through A in the direction of the vector (1, 2, 2).
c)The moment due to each force about the point C.


What have you done so far, and where are you stuck?

Post any relevant working.
Reply 2
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Original post by ghostwalker
What have you done so far, and where are you stuck?

Post any relevant working.

I haven’t done any calculations. I don’t even know how to start solving it.
Original post by chidzix
I haven’t done any calculations. I don’t even know how to start solving it.

I find that somewhat surprising.

a) To get the resultant. You need to add the two forces. The second one is already in vector format. Can you convert the first one into vector format?
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Original post by ghostwalker
I find that somewhat surprising.

a) To get the resultant. You need to add the two forces. The second one is already in vector format. Can you convert the first one into vector format?

You should be able to using unit vectors
how do you find the magnitude of the vector?
Reply 6
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Original post by ThiagoBrigido
how do you find the magnitude of the vector?

You square each vector component then square root it(Pythagorus theorem)
Original post by chidzix
You should be able to using unit vectors


Not clear what you mean by that, but if you're able to convert it into (x,y,z) format, then do so.
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Original post by ghostwalker
Not clear what you mean by that, but if you're able to convert it into (x,y,z) format, then do so.

How would you calculate b?
Original post by chidzix
How would you calculate b?


I assume you now have the resultant - we'll call it R.

You're looking to project R onto the direction (1,2,2).

First off you want a unit vector in that direction - I'll call it n. I presume you can calculate that.

Then, the magnitude of the component of R in that direction is simply the dot product R.n

And if you require it in vector format it's (R.n)n where R.n is simply the scalar multiple of n.
(edited 3 years ago)
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Original post by ghostwalker
I assume you now have the resultant - we'll call it R.

You're looking to project R onto the direction (1,2,2).

First off you want a unit vector in that direction - I'll call it n. I presume you can calculate that.

Then, the magnitude of the component of R in that direction is simply the dot product R.n

And if you require it in vector format it's (R.n)n where R.n is simply the scalar multiple of n.

The unit vector. Is it for (1,2,2) or R.
Original post by chidzix
The unit vector. Is it for (1,2,2) or R.


(1,2,2), the direction in which you're resolving.
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Original post by ghostwalker
(1,2,2), the direction in which you're resolving.

Cheers. By any chance do you have any idea on calculating C
Original post by chidzix
Cheers. By any chance do you have any idea on calculating C


In 3D the moment of a force is usually calculated via the cross product.

So, you want rXF for each of the two forces. Where r is the vector from the place where you're taking moments (in this case C) to a point on the line of action of the force, in this case A will do; and F is the force, of course.
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Original post by ghostwalker
In 3D the moment of a force is usually calculated via the cross product.

So, you want rXF for each of the two forces. Where r is the vector from the place where you're taking moments (in this case C) to a point on the line of action of the force, in this case A will do; and F is the force, of course.

So to find r. Do we subtract the vector A from C and use AC as R
Original post by chidzix
So to find r. Do we subtract the vector A from C and use AC as R


Other way round. You want CA, since C is the point about which you're finding the moment, and that's your r.
Reply 16
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Original post by ghostwalker
Other way round. You want CA, since C is the point about which you're finding the moment, and that's your r.

So r will be the same for each force.
Original post by chidzix
So r will be the same for each force.


Yes, since they're both acting through the point A.
Reply 18
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Original post by ghostwalker
Yes, since they're both acting through the point A.

Cheers.

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