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# Vectors watch

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1. Given that a = i - 2j and b = -3i + j

find x if a+xb is parallel to the vector:
-i - 3j

many thanks
2. If two vectors are parallel, you can find one from the other by multiplying by a constant. So (a+xb)=k(-i-3j)
3. i'm still a little confussed
4. hello there.

you want to find x.

So first calculate ax + b = x(1,-2) + (-3,1) = (x,-2x) + (-3,1) = (x-3,1-2x).

You know that (x-3,1-2x) is parallel to (-1,-3). For 2 vectors to be parallel , they must have the same DIRECTION.

Hence, the vector (x-3,1-2x) must have the same direction as (-1,-3).

See if you can work it out now
5. (a+xb)=k(-i-3j)

(a+xb)=i-2j + x(-3i+j)

Rearrange k(-i-3j)=i-2j + x(-3i+j)

to get i and j components. You'll get two simultaneous equations in x and k
6. you wont need to use the multiple of k. Technically that is correct, but since you're being asked for a value of x, I'd just set the two vectors equal to one another. They will then have to have the same direction. But Triangulor is correct, if you take any multiple of the direction vector, they will still be parallel.

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Updated: October 9, 2006
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