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Parallel vectors Mechanics

I don’t understand how they’ve used the information that the vector is parallel to the vector (2i+j) in their answer can someone pleas explain?.. (for part c)
E8407913-D5EE-4547-BA86-10DDF439F6A3.jpeg
D8B42DB6-6C01-4B12-B531-B1C7D73E9D85.jpeg
Reply 1
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mqb2766
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Original post by hiya
I don’t understand how they’ve used the information that the vector is parallel to the vector (2i+j) in their answer can someone pleas explain?.. (for part c)
E8407913-D5EE-4547-BA86-10DDF439F6A3.jpeg
D8B42DB6-6C01-4B12-B531-B1C7D73E9D85.jpeg

If it's moving parallel to the vector, then then they both have the same gradient.
As t changes, the gradient of v is 6/4 = 1.5, so parallel to the vector.
Reply 2
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hiy\a
OP
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Original post by mqb2766
If it's moving parallel to the vector, then then they both have the same gradient.
As t changes, the gradient of v is 6/4 = 1.5, so parallel to the vector.


Im sorry i still dont understand how theyve used this in the answer shown :frown:
Original post by hiya
Im sorry i still dont understand how theyve used this in the answer shown :frown:

They haven't (I'm not sure what mqb was thinking, TBH).

If a vector xi + yj is parallel to 2i + j, then the i component must be twice the j component (the same as is true for 2i + j). In other words, x = 2y.

See if you can see how they've used this in their answer.
Reply 4
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hiy\a
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Original post by DFranklin
They haven't (I'm not sure what mqb was thinking, TBH).

If a vector xi + yj is parallel to 2i + j, then the i component must be twice the j component (the same as is true for 2i + j). In other words, x = 2y.

See if you can see how they've used this in their answer.

If the i component is twice the j component wouldnt it be x=2y?
Original post by hiya
If the i component is twice the j component wouldnt it be x=2y?

Isn't that exactly what I wrote?
Reply 6
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hiy\a
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Original post by DFranklin
Isn't that exactly what I wrote?

Sorry I meant 2x=y
Original post by hiya
Sorry I meant 2x=y

if x = 2, y =1, then the x-component (i-component) is twice the y-component, agreed?

Does x = 2y, or y = 2x?
Reply 8
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hiy\a
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Original post by DFranklin
if x = 2, y =1, then the x-component (i-component) is twice the y-component, agreed?

Does x = 2y, or y = 2x?

Y=2x?
Original post by hiya
Y=2x?

x = 2, y = 1 and you think y = 2x?
Reply 10
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hiy\a
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Original post by DFranklin
x = 2, y = 1 and you think y = 2x?

Because x is double y?
Original post by hiya
Because x is double y?

If x is double y then x = 2y, surely?

Look: I get the wording of some of this can be confusing, but the bottom line is: x= 2, y = 1. It should not be difficult to go from there and work out which of x = 2y or y = 2x is the correct statement.

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