Vectors question: is the mark scheme wrong?

[shuphie]

MY OWN WORKING:

Why I'm confused:
The yellow parts are where the mark scheme differs, the mark scheme says that AB = b+a when I calculated b-a
The mark scheme then uses this in the end, because we make OP from AB, so OP in my answer 3/10 (b-a), but for theres they would use b+a
This causes them to get from 1 + 3/10 = x, x=7/10 while I get 13/10
Is my answer wrong? Where? Thank you

 

[Dr.Peterson]

View attachment 36861
MY OWN WORKING:
View attachment 36863
Why I'm confused:
The yellow parts are where the mark scheme differs, the mark scheme says that AB = b+a when I calculated b-a
The mark scheme then uses this in the end, because we make OP from AB, so OP in my answer 3/10 (b-a), but for theres they would use b+a
This causes them to get from 1 + 3/10 = x, x=7/10 while I get 13/10
Is my answer wrong? Where? Thank you

You're right that AB = b - a; and from that you correctly calculated that OP = 3/10 a + 3/10 b:

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Then you wrongly wrote that OP = 3/10(a - b):

​

Why? If you correct that to 3/10 (a + b), everything should work out.

OP is not a multiple of AB, but of OM. Right?

 

[shuphie]

You're right that AB = b - a; and from that you correctly calculated that OP = 3/10 a + 3/10 b:

View attachment 36864​

Then you wrongly wrote that OP = 3/10(a - b):

View attachment 36865​

Why? If you correct that to 3/10 (a + b), everything should work out.

OP is not a multiple of AB, but of OM. Right

Thank you