In this video, we will explore vector basics and unit vectors in three-dimensional space. A vector is a directed line segment represented as an arrow with a specific length and direction. Vectors going in opposite directions or having different lengths are considered different. Equivalent vectors point in the same direction and have the same length, regardless of their position.
Unit vectors are vectors with a length of one and are used to build other vectors. In a 3D coordinate system, unit vectors run along each directional axis (x, y, z). The unit vector along the x-axis is often denoted as i, along the y-axis as j, and along the z-axis as k. They have specific components i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1). Any vector can be expressed as a linear combination of these unit vectors.
Exercise 1
Express the vector v = 2i using the unit vector notation.
Solution
v = 2i = 2(1, 0, 0) = (2, 0, 0)
Exercise 2
Represent the vector w = 3k in terms of the unit vector notation.
Solution
w = 3k = 3(0, 0, 1) = (0, 0, 3)
Exercise 3
Write the vector v = (0, 1, 0) as a scalar multiple of the unit vector j.
Solution
v = (0, 1, 0) = 1/2j = (0, 1/2, 0)
Remember, unit vectors are building blocks for other vectors. Stay tuned for more videos. Don't forget to like, subscribe, and thank you for watching!
Buy a clever and unique math t-shirt: [ Ссылка ] Please visit our Merch Stores and help support the spreading of knowledge:)
Our T-Shirt Merch:
[ Ссылка ]
Our Amazon Store for Awesome Merch too:
[ Ссылка ] Amazon Music Free Trial: [ Ссылка ]
Amazon Prime Free Trial: [ Ссылка ]
Audible Plus Free Trial: [ Ссылка ]
Kindle Unlimited Free Trial: [ Ссылка ] Video Game Bestsellers: [ Ссылка ] Are you a fan of our content and want to support us in a tangible way? Why not check out our merchandise? We have a wide range of products, including t-shirts, hoodies, phone cases, stickers, and more, all featuring designs inspired by our brand and message.By purchasing our merchandise, not only will you be showing your support for our work, but you'll also be able to enjoy high-quality, stylish products that you can wear or use in your daily life. And best of all, a portion of the proceeds goes directly towards helping us continue to create and produce the content you love.So what are you waiting for? Head over to our online store now and browse our selection of merchandise. We're sure you'll find something you love.
