If you like what you see in Mathguru
Subscribe Today
 For 12 Months US Dollars 12 / Indian Rupees 600 Available in 20 more currencies if you pay with PayPal. Buy Now No questions asked full moneyback guarantee within 7 days of purchase, in case of Visa and Mastercard payment

Example:Finding Value of Unknown for Perpendicular Vectors

 Post to:

Explanation:

Orthogonality

Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.

Mathematics

In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle.

Euclidean vector spaces

In 2- or higher-dimensional Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians. Hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces. In terms of Euclidean subspaces, the orthogonal complement of a line is the plane perpendicular to it, and vice versa. Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin. (Our solved example in mathguru.com uses this concept)

Examples

The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal to each other, since (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, and (1)(1/3) + (3)(1) + (2)(−5/3) = 0.

http://en.wikipedia.org/wiki/Orthogonality#Euclidean_vector_spaces