dividing vectors: (63i+56j)=(9i+8j)t is equal to 7i+7j = t

[petr]

hello,

(63i+56j)=(9i+8j)t

is equal to 7i+7j = t
in my study book is after written t equals 7 seconds. they got it from this statement 7i+7j = t

but the resultant time of this two dimensional vector is its magnitude so if i wanna get resultant value wouldn't it be root of 49 + 49 which is 9.89?

 

[Ishuda]

hello,

(63i+56j)=(9i+8j)t

is equal to 7i+7j = t
in my study book is after written t equals 7 seconds. they got it from this statement 7i+7j = t

but the resultant time of this two dimensional vector is its magnitude so if i wanna get resultant value wouldn't it be root of 49 + 49 which is 9.89?

No. t is just the 'elapsed time from zero' or something equivalent to that. Thus
(a i + b j) = (9i + 8j) t
which we can also write as
(a i, b j) = (9i, 8j) t
for some variable t.

EDIT: Correct mistake and (hopefully make clearer)

 

[petr]

what you mean? elapsed time from zero. I dont get it could you try to explain it in different way, thank you.

i don't understand particularly the thing 7i + 7j = 7, this is just a step I do. In the exam book they skip it and take it out of the complete expression of (63i+56j) = t(9i+8j)

 

[Ishuda]

what you mean? elapsed time from zero. I dont get it could you try to explain it in different way, thank you.

i don't understand particularly the thing 7i + 7j = 7, this is just a step I do. In the exam book they skip it and take it out of the complete expression of (63i+56j) = t(9i+8j)

What does t stand for? It could stand for time, or any other independent variable. The point is we have a vector function v
v(t) = (9 i, 8 j) t
where t is the independent variable. I was just calling t time but it isn't necessarily that.

What you are doing is equating the i and j components, i.e. 63i = 9ti and 56j=9tj. This gives a t of 7 so that
v(7) = (9 i, 8 j) 7 = (63 i, 56 j)

 

[pka]

**(63i+56j)=(9i+8j)t
is equal to 7i+7j = t FALSE, FALSE & FALSE

The reason being that is a TYPE ERROR. The expression \(\displaystyle 7\bf{i}+7\bf{j}\) is a vector whereas \(\displaystyle t\) is a scalar. They cannot be equal, that would be a type-error.
What would make ** true? Well if \(\displaystyle \Large\bf{t=7}~?\)

 

[petr]

and here we go

hohoho and here we go.

(63i+56j)=(9i+8j)t
root of(63^2+56^2) / root of (9^2+8^2) = t

so thanks boys it was lovely to work with you :]

 

[pka]

hohoho and here we go.
(63i+56j)=(9i+8j)t
root of(63^2+56^2) / root of (9^2+8^2) = t

I wish you understood vectors. But it clear that you don't.
This topic is so important that you owe it to yourself to try.