# How do you find a vector of length 10 that is oppositely directed to u=3i-4j?

Jul 14, 2016

A vector of length $10$ that is oppositely directed to u=3i-4j is $- 6 i + 8 j$

#### Explanation:

A vector oppositely directed to $u = 3 i - 4 j$ is $v = - u = - \left(3 i - 4 j\right)$ i.e. $v = - 3 i + 4 j$.

However, its length is given by $| v | = \sqrt{{\left(- 3\right)}^{2} + {4}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

What we desire is a vector of length $10$ that is double of $v$ and hence

A vector of length $10$ that is oppositely directed to u=3i-4j is $2 v = 2 \cdot \left(- 3 i + 4 j\right) = - 6 i + 8 j$