How do I find the direction angle of a vector?

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Let $v= -3 i-10j$. I found the dot product to be $109$ and the magnitude to be $\sqrt{11881}$. I divided it out and it came out to be one. I don't know what I'm doing wrong. Please help.

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A couple of things: (a) Isn't the dot-product an operation defined between 2 different vectors? If so, it's not clear in your example what the 2nd vector is. (b) Have you graphed this vector with respect to the origin on an XY-graph? After doing that, it should be a matter of employing well-known trigonometric rules to find out the "angle of the vector".