omgimfailing
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This is the maths question I need help on

Given that the resultant of the vectors a=2pi-5j and b=6i-3pj is parallel to the vector x=4i-5j,

Find the value of a

And find the resultant of the vectors a and b
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Pangol
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(Original post by omgimfailing)
This is the maths question I need help on

Given that the resultant of the vectors a=2pi-5j and b=6i-3pj is parallel to the vector x=4i-5j,

Find the value of a

And find the resultant of the vectors a and b
If two vectors u and v are parallel to each other, there is a constant t such that u = tv. So, for example, the vectors u = 4i - 2j and v = 2i - j are parallel becasue u = 2v.

But another way of looking at this is to say that the ratio of the j component to the i component of each vector is the same. In u, this is -2/4, and in v, this is -1/2. Because -2/4 = -1/2, the vectors are parallel. Think of this as saying that when you take the journey given be each vector, you move the same distance upwards (or downward) for each step to the right.

I think this is the easiest way to do this question. Work out the resultant of a and b in terms of p (I think you mean to find the value of p, not a), and then consider this ratio. It should be the same as the ratio of the j component of x to the i component of x. This will give you a fairly simple equation to solve.
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omgimfailing
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could you do a worked example, i dont understand
(Original post by Pangol)
If two vectors u and v are parallel to each other, there is a constant t such that u = tv. So, for example, the vectors u = 4i - 2j and v = 2i - j are parallel becasue u = 2v.

But another way of looking at this is to say that the ratio of the j component to the i component of each vector is the same. In u, this is -2/4, and in v, this is -1/2. Because -2/4 = -1/2, the vectors are parallel. Think of this as saying that when you take the journey given be each vector, you move the same distance upwards (or downward) for each step to the right.

I think this is the easiest way to do this question. Work out the resultant of a and b in terms of p (I think you mean to find the value of p, not a), and then consider this ratio. It should be the same as the ratio of the j component of x to the i component of x. This will give you a fairly simple equation to solve.
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Pangol
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(Original post by omgimfailing)
could you do a worked example, i dont understand
I thought I just had!

In the example I gave, u = 4i - 2j. The i component it 4, and the j component is -2. So the ratio of the j component to the i component is -2/4.

The other vector in the example is 2i - j. So the ratio of the j component to the i component is -1/2.

Because these ratios are the same, the vectors are parallel.

In your question, one of the vectors is 4i - 5j. So, the ratio os the j component to the i component is -5/4. Your other vector is the resultant of 2pi - 5j and 6i - 3pj. What is the resultant of these vectors? Find that first, then find the ratio of the j component to the i component, and then put this equal to -5/4.
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omgimfailing
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Ohhh thank you I understand now, much appreciated!
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