Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (-3, -3) and arrived in the Iron Hills at the point with coordinates (-2, 2). If he began walking in the direction of the vector v=3I+2J and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn.

Question

e.mccormick · Answer

OK, what part of the question do you not get?

anonymous · Answer

not sure how to interpret a vector from an equation, v=3I+2J

e.mccormick · Answer

OK.... have you looked at component vectors or any of the stuff for graphing the i,j,k stuff?

anonymous · Answer

I feel like the only time ive seen vectors they have been in a form like (3,5,1)

e.mccormick · Answer

Same basic stuff, but with two components, so in a plane.

anonymous · Answer

Please explain further. I'm still lost

e.mccormick · Answer

Trying to find a good example...

e.mccormick · Answer

One way to look at is in standard position: http://www.wolframalpha.com/input/?i=vector+3i+%2B+2j&dataset=&asynchronous=false&equal=Submit

anonymous · Answer

OK but how do you interpret that equation and know how to draw a vector from it.

e.mccormick · Answer

You have their starting point and that vector makes a line with direction from that starting point.  What they are asking is where would that line intersect another line at $90^{\circ}$ where the second line touches the destination.

e.mccormick · Answer

If you think about it, you have the old perpendicular lines problem from geometry, but being done with vectors and points.

anonymous · Answer

Yes but i dont know how to look at v=3I+2J and draw a graph of it. How do I do that?

e.mccormick · Answer

That WolframAlpha page should have a vector plot on it and show the slope.  the i,j,k are unit components of a vector.  If they are standard units, which they usually are, then they are just how many over and up for i and j.

e.mccormick · Answer

To link it back with the old geometry terms: i is units in x and j is units in y.  So your rules for slope as rise over run can be applied.

anonymous · Answer

ah... but what is k in that equation?

e.mccormick · Answer

This one was just a 2d plot.  No k. Or k=0.

anonymous · Answer

and the starting point was just (-3,-3) correct?

e.mccormick · Answer

Yah.  That is given.

anonymous · Answer

Im still a little lost on how to actually solve the problem though: (

e.mccormick · Answer

OK.  Hmm... well, it all comes down to this:  They make a 90 degree turn.  If you make a 90 degree turn, it means you have a vector or line with a negative inverse slope.  They want the point of intersection of the two lines or the point where you change slope.  If you graph the two points and start graphing copies of the vector from the start point, this one should be pretty obvious.

e.mccormick · Answer

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e.mccormick · Answer

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e.mccormick · Answer

If I use these to do something like what you are doing.  I could end up with this:
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