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How can we define simply that velocity is a vector quantity without mentioning that velocity has vector properties. How can we simply say it needs both magnitude and direction for its complete description? Well for magnitude it is clear but for direction being a necessary for its complete description I found it hard clear the concept on the subject?

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    $\begingroup$ That's just a definition. Are you saying you don't like it? $\endgroup$ – auxsvr May 4 '14 at 12:26
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I will ask you a simple question. You are moving with speed $5m/s$ and I'm moving with speed $10m/s$. What is my relative speed from your point of view? Immediately you first reaction is: "I cannot answer because I have no idea if you are moving in my direction or away from me." And that would be correct, because the answer changes, it depends on the direction. If I'm moving away from you, the answer is $10 + 5 = 15 m/s$. If I'm moving in your direction the answer is $10 - 5 = 5 m/s$. This is why we say velocity has magnitude (e.g $5m/s$) and direction (e.g away from you etc.), to avoid confusions like this.

Edit: To expand, the direction can be arbitrary, it can be in the x, y, z direction or any combination of those. Therefore we need a vector to fully describe the velocity. A vector therefore would be a powerful tool which will allow you to manipulate velocities without thinking too hard about angles with respect to you and such.

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By definition velocity is a vector quantity. Speed is defined as the magnitude of that vector. If you wanted to speak about it without mentioning the vector quantity you would simply talk about speed.

In everyday, non-physics speech, velocity is confused with speed. To physicists, velocity is by definition a vector. The direction is required if you wish to understand what the speed is relative to other objects or points of reference.

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