If you are a student of Mathematics, you've definitely come across Vectors at some point of your study. Vectors are used extensively, both in Physics and Mathematics. So utilise these tips on Vectors.
I have taught High School and College Mathematics, for close to three decades and I can confidently guide you with Authority for Class 12 Mathematics. So, even if you don't go for private tutoring, no worries, this is for you!
So what is a vector? A vector is a quantity which has both magnitude and direction. The magnitude of a vector is also called its modulus and is defined as follows.
![modulus of a vector](https://static.wixstatic.com/media/f00b62_76105ff6ff6447ae9b820ee279a3a5fb~mv2.jpg/v1/fill/w_750,h_1125,al_c,q_85,enc_auto/f00b62_76105ff6ff6447ae9b820ee279a3a5fb~mv2.jpg)
You'll need to note that while calculating vectors, it is final point- initial point.
![vector notation](https://static.wixstatic.com/media/f00b62_1e6707b54dfb44b287d45b5731bb00a7~mv2.jpg/v1/fill/w_750,h_1125,al_c,q_85,enc_auto/f00b62_1e6707b54dfb44b287d45b5731bb00a7~mv2.jpg)
Next, you'll proceed to learn about direction angles or direction ratios and how to compute the direction cosines given the direction ratios. An important property of direction cosines is also illustrated here.
![direction ratios of a vector](https://static.wixstatic.com/media/f00b62_c456a3d6c79245cbab4b17d7fb3866cd~mv2.jpg/v1/fill/w_750,h_1125,al_c,q_85,enc_auto/f00b62_c456a3d6c79245cbab4b17d7fb3866cd~mv2.jpg)
![direction cosines of a vector](https://static.wixstatic.com/media/f00b62_110cf57de95b40aaa01ed296e24b9961~mv2.jpg/v1/fill/w_750,h_1125,al_c,q_85,enc_auto/f00b62_110cf57de95b40aaa01ed296e24b9961~mv2.jpg)
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