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# P3 vectors- we wouldn't get anything like this, would we? watch

1. P3 green heinemann book- page 175
This is just the first part of the question....

16. The point P lies on the line which is parallel to the vector 2i + j - k and which passes through the position vector i + j + 2k.
The point Q lies on another line which is parallel to the vector i + j - 2k and which passes through the point with position vector
i + j + 4k.
The line PQ is perpendicular to both these lines. Find a vector equation of the line PQ....

now i don't know if i took a really long, complicated route in trying to figure this out, but in any case it took me a hell of a long time to do.
i'm guessing this question was written back in the old days with 3 hr exams, right?
2. (Original post by mockel)
P3 green heinemann book- page 175
This is just the first part of the question....

16. The point P lies on the line which is parallel to the vector 2i + j - k and which passes through the position vector i + j + 2k.
The point Q lies on another line which is parallel to the vector i + j - 2k and which passes through the point with position vector
i + j + 4k.
The line PQ is perpendicular to both these lines. Find a vector equation of the line PQ....

now i don't know if i took a really long, complicated route in trying to figure this out, but in any case it took me a hell of a long time to do.
i'm guessing this question was written back in the old days with 3 hr exams, right?
well the way i'd do it is to set coordinates for P and Q as (x1,y1,z1) = (1+2s,1+s,2-s) and (x2,y2,z2) = (1+t,1+t,4-2t)resp. then get an expression for PQ, and say that when that is dot product'ed with each of the two lines, it will equal 0.
so now you just solve the simultaneous equation to get s and t, and there's your answer. i don't know how long it'd take to do that tho...

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