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The magnitude of (i + 2j) is sqrt(5).

The magnitude of your new vector is 2.

If both vectors are in the same direction, then each component of one vector is

in the same ratio to the corresponding component of the other one.

The components of the known vector are 1 and 2, and its magnitude is sqrt(5).

The magnitude of the new one is 2/sqrt(5) times the magnitude of the old one.

So its x-component is 2/sqrt(5) times i, and its y-component is 2/sqrt(5) times 2j.

The new vector is [ (2/sqrt(5))i + (4/sqrt(5))j ].

Since the components of both vectors are proportional, they're in the same direction.

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Q: How do you find the vector of magnitude 2 in the direction of vector i plus 2j?
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