Finding the unit vector

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Introduction to Unit Vectors

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Find the unit vector of $\vec{a}=$ $a =$ < $6,-8$ $6, - 8$ >, and verify
What is a unit vector which has the same direction as $\vec{b}=3i+4j$ $b = 3 i + 4 j$ ?
Given $\vec{v}=$ $v =$ < $10,-3$ $10, - 3$ > and $\vec{w}=$ $w =$ < $-6,8$ $- 6, 8$ >,
1. find $\vec{v}+\vec{w}$
2. find the unit vector of the resultant vector
Given $\vec{v}=$ $v =$ < $-5,6$ $- 5, 6$ > and $\vec{w}=$ $w =$ < $7,4$ $7, 4$ >,
1. find $\vec{v}-\vec{w}$
2. find the unit vector of the resultant vector

Topic Notes

In this section, we will learn what is a unit vector, which literally refers to a vector with magnitude of 1 unit. We will practice on calculating a unit vector as well as exploring how this concept relates to the basic unit vectors that are found in vectors represented in rectangular form.

Unit Vector = a vector with a magnitude of 1
Given vector

\vec{v}

, the unit vector in the direction of vector

\vec{v}

is obtained as follows:

\hat{u}=\frac{\vec{v}}{||\vec{v}||}

where

||\hat{u}||=1

Unit vector

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Unit vector

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