where did (1, 2, 1) come from on part b)ii? I used (2, 4, 2) and still got the right answer.
That's because (2, 4, 2) is a multiple of (1, 2, 1) - both have the equivalent direction just different sizes, and it's only the direction that you care about.
The mark scheme is just using 1/2 the vector you did but it doesn't make a difference to the angle between them. You can make the vector as long as you want and you'll see that in the calculation it cancels out o give the right answer.
That's because (2, 4, 2) is a multiple of (1, 2, 1) - both have the equivalent direction just different sizes, and it's only the direction that you care about.
So would i still get a mark for my answer?
Have they just simplified the vector like with a fraction?
That's better but I feel you would be better off without drawing an axis - it is restricting your diagrams. Also you are not told that angle OAB is 90 so it's best not to assume it.
I'm going to post a diagram I've made again:
The key things we know for sure are that the line l is parallel to AB, angle ODC is 90 and OC = 2OB so this is all shown on the diagram.
SInce OD and AB are perpendicular, it is true that OD⋅AB=0.
You already have AB and you know that OD is the position vector of a point that lies on l. Any ideas how to carry on?
That's better but I feel you would be better off without drawing an axis - it is restricting your diagrams. Also you are not told that angle OAB is 90 so it's best not to assume it.
I'm going to post a diagram I've made again:
The key things we know for sure are that the line l is parallel to AB, angle ODC is 90 and OC = 2OB so this is all shown on the diagram.
SInce OD and AB are perpendicular, it is true that OD⋅AB=0.
You already have AB and you know that OD is the position vector of a point that lies on l. Any ideas how to carry on?
I cant see your diagram right now but would you do the dot product of AB and OD = 0 ?
That's better but I feel you would be better off without drawing an axis - it is restricting your diagrams. Also you are not told that angle OAB is 90 so it's best not to assume it.
I'm going to post a diagram I've made again:
The key things we know for sure are that the line l is parallel to AB, angle ODC is 90 and OC = 2OB so this is all shown on the diagram.
SInce OD and AB are perpendicular, it is true that OD⋅AB=0.
You already have AB and you know that OD is the position vector of a point that lies on l. Any ideas how to carry on?
I know it doesnt say but if OD and AB are perpendicular then isnt angle OAB = 90?
That seems okay at first glance - did you get the right answer?
And do you understand the working?
I'm on my phone so can't properly help today but I can tomorrow.
Oh thats ok, i appreciate your help
Yeah i got it right but i would have initially used the dot product of OD and DC (not AB) because like you said, it mentions that ODC = 90 so they are definitely perpendicular.
If 2 lines are perpendicular doesnt that mean the angle between is 90?
Oh thats ok, i appreciate your help
Yeah i got it right but i would have initially used the dot product of OD and DC (not AB) because like you said, it mentions that ODC = 90 so they are definitely perpendicular.
You said OAB is a right angle. This would mean that OA and AB are perpendicular but you are not told this.
I'm on my phone so someone will hopefully correct me if I'm talking rubbish