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junior college 1 | H2 Maths
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Hi! I know the question is not provided here but i would like to ask Why did the answer key give the ratio RB=-3/2 AR? (line 4)
My answer is RB=-2/3 AR... :( Can someone explain to me this reasoning behind the answer key?
Thanks so muchhhh:D
Date Posted: 4 years ago
Views: 322
let C be point (1,8,-9)
then
AR = 2 x OC ... [read all as vectors]
OC = (1/2) x AR
and
RB = -3 x OC
= -3 x (1/2) x AR
= -(3/2) AR
then
AR = 2 x OC ... [read all as vectors]
OC = (1/2) x AR
and
RB = -3 x OC
= -3 x (1/2) x AR
= -(3/2) AR
RB = -3(1 8 -9)
= -3/2 (2 (1 8 -9) )
= -3/2 AR
= -3/2 (2 (1 8 -9) )
= -3/2 AR
If RB = -⅔AR,
Then RB = -⅔ (2 (1 8 -9) )
= -4/3 (1 8 - 9)
That results in a contradiction since RB = -3/2 (1 8 -9), which ≠ -4/3 (1 8 -9)
Then RB = -⅔ (2 (1 8 -9) )
= -4/3 (1 8 - 9)
That results in a contradiction since RB = -3/2 (1 8 -9), which ≠ -4/3 (1 8 -9)
Good evening Sonia! You can think of the vector as “x”.
RB = -3x
AR = 2x
RB/AR
= -3x / 2x
= -3/2
RB = -3x
AR = 2x
RB/AR
= -3x / 2x
= -3/2
The problem with that is, you can't divide a vector by another.
Or using the primary school idea “units” should suffice for the given answer.
The negative sign is merely representing that the vector RB is in the opposite direction of AR.
The coefficient represents magnitude with respect to the vector. Since RB has a coefficient of 3(ignoring the - sign) and AR has a coefficient of 2, and their vectors are the same,
then RB's magnitude is simply 3/2 of AR's.
Add the negative sign,
RB = -3/2 AR
i.e RB is a vector parallel to and with magnitude 3 times of AR, but in the opposite direction
(Strictly speaking we could call them antiparallel vectors)
The coefficient represents magnitude with respect to the vector. Since RB has a coefficient of 3(ignoring the - sign) and AR has a coefficient of 2, and their vectors are the same,
then RB's magnitude is simply 3/2 of AR's.
Add the negative sign,
RB = -3/2 AR
i.e RB is a vector parallel to and with magnitude 3 times of AR, but in the opposite direction
(Strictly speaking we could call them antiparallel vectors)
See 1 Answer
done
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If you take -3/2 and multiply it with the AR, you will end up with RB. This is why the answer sheet is correct.
Date Posted:
4 years ago
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