# Find the value of t for which BQM is a straight line

#1
Question (part c): http://prntscr.com/s7jyig
My w/o: http://prntscr.com/s7k0hx

I don't see how I can find the value of t unless I know the value of s...
Last edited by TSR360; 2 years ago
0
2 years ago
#2
(Original post by TSR360)
Question (part c): http://prntscr.com/s7jyig
My w/o: http://prntscr.com/s7k0hx

I don't see how I can find the value of t unless I know the value of s...
Vectors are linearly independent, so it is sufficient for you to compare coefficients of these vectors between both sides and hence solve for simultaneously.
Last edited by RDKGames; 2 years ago
0
2 years ago
#3
(Original post by TSR360)
Question (part c): http://prntscr.com/s7jyig
My w/o: http://prntscr.com/s7k0hx

I don't see how I can find the value of t unless I know the value of s...
A simpler approach, without ever needing to even introduce , is to observe how the coefficients of in are related (they are just numbers, so the observation should be simple) and impose the same condition on when written in a similar form.

I.e.

note that the coefficient of is exactly -1/2 lots of the coefficient of .

Impose the same condition on the vector .

Is it clear?
0
#4
(Original post by RDKGames)
A simpler approach, without ever needing to even introduce , is to observe how the coefficients of in are related (they are just numbers, so the observation should be simple) and impose the same condition on when written in a similar form.

I.e.

note that the coefficient of is exactly -1/2 lots of the coefficient of .

Impose the same condition on the vector .

Is it clear?
no...
0
2 years ago
#5
(Original post by TSR360)
no...
Clearly, and must be parallel AND go in the same direction, in order to constitute one straight line .

What makes to vectors parallel? You could say one vector being a multiple of the other, but in a more fundamental level, it's when you spot a multiplicative relationship between the components. You can think of this multiplicative relationship as the ratio between the two components. Any parallel vector must preserve it.

E.g. if , then the component is -2 lots of the component. This property will not change when you scale the vector .

is parallel to but it's and the property discussed above still holds true.

is parallel to but it's and the property above still holds true.

Thus, in this question it is much simpler to exploit the property relating the coefficients of rather than introduce a new variable .

Clear now?
Last edited by RDKGames; 2 years ago
0
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