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# What's wrong with this? (Vectors) watch

1. The question said "whats the shortest distance between A and the line OB?"

So line OB is
Now I tryed to find the distance using pythag.

surely, because any number squared is positive, the shortest distance is when lambda equals 0. so i got

but the mark scheme did
(we had to work out sin(theta) earlier)
I'm strugling to picture the 3 dimensions in my head. how does the sin work? and why doesn't my method work?
2. (Original post by hello calum)
The question said "whats the shortest distance between A and the line OB?"

So line OB is <-------
Now I tryed to find the distance using pythag.

surely, because any number squared is positive, the shortest distance is when lambda equals 0. so i got

but the mark scheme did
(we had to work out sin(theta) earlier)
I'm strugling to picture the 3 dimensions in my head. how does the sin work? and why doesn't my method work?
Just there.
3. The direction from A to a general point on OB is (i+5j-k)-L(2i+j-2k).

The dot product of this with 2i+j-2k needs to be zero.
4. Remember that the shortest distance is always a perpendicular line.

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Updated: January 3, 2013
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