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M1 paper vectors question - help


I can't do the last part of the question and I don't understand how they got there from looking at the mark scheme. Please could someone help? :confused:
Screen Shot 2015-04-10 at 22.42.15.png107.2KB
Original post by 1lilypad1

I can't do the last part of the question and I don't understand how they got there from looking at the mark scheme. Please could someone help? :confused:

7cii)?
OQ=OP+λ(−i+j)OQ = OP + \lambda(-i + j)(because it's north-west of P).
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1lilypad1
OP
7
Original post by morgan8002
7cii)?
OQ=OP+λ(−i+j)OQ = OP + \lambda(-i + j)(because it's north-west of P).


I don't understand that I'm afraid. How can you use it to find the time?
Original post by 1lilypad1
I don't understand that I'm afraid. How can you use it to find the time?


p=(i+j)+t(2i−3j)=(1+2t)i+(1−3t)jp = (i+j) + t(2i-3j) = (1 + 2t)i + (1 - 3t)j
q=(−2j)+t(3i+4j)=(3t)i+(−2+4t)jq = (-2j) + t(3i + 4j) = (3t)i + (-2 + 4t)j

Unparseable latex formula:

q = p + \lamda(-i + j)


(3t)i+(−2+4t)j=(1+2t)i+(1−3t)j+λ(−i+j)(3t)i + (-2+4t)j = (1+2t)i + (1-3t)j + \lambda(-i + j)
(−1+t)i+(−3+7t)j=λ(−i+j)(-1 + t)i + (-3 + 7t)j = \lambda(-i+j)
O(i)O(i) −1+t=−λ-1+t = -\lambda
O(j)O(j) −3+7t=λ-3+7t = \lambda


∴−1+t=−(−3+7t)\therefore -1 + t = -(-3+7t)

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