# Find a Vector

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• Oct 4th 2008, 04:05 AM
magentarita
Find a Vector
Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.

• Oct 4th 2008, 05:02 AM
earboth
Quote:

Originally Posted by magentarita
Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.

The vector $\vec p = i+j$ has the magnitude $|i+j| = \sqrt{2}$

Therefore the vector $\vec u = \frac1{\sqrt{2}} (i+j)$ has the magnitude 1. (It's a unit vector)

And therefore the vector $\vec v = 3 \cdot \frac1{\sqrt{2}} (i+j) = \left(\frac{3\sqrt{2}}2i + \frac{3\sqrt{2}}2 j \right)$
• Oct 4th 2008, 05:54 AM
magentarita
ok.....
Quote:

Originally Posted by earboth
The vector $\vec p = i+j$ has the magnitude $|i+j| = \sqrt{2}$

Therefore the vector $\vec u = \frac1{\sqrt{2}} (i+j)$ has the magnitude 1. (It's a unit vector)

And therefore the vector $\vec v = 3 \cdot \frac1{\sqrt{2}} (i+j) = \left(\frac{3\sqrt{2}}2i + \frac{3\sqrt{2}}2 j \right)$

I did not know about that formula. Great stuff here.

Thanks