Distance and Dot Products: Consider the vectors ='false' u= \langle 3,10,9 \rangle and, v=...


Distance and Dot Products: Consider the vectors {eq}u= \langle 3,10,9 \rangle and, v= \langle 9,-5,7\rangle . {/eq}

{eq}Compute \|u \|= {/eq}

{eq}Compute \| v \| = {/eq}

Compute u-v =

Vector Magnitude and Difference:

For the difference between the vector in three-dimensional space, we'll subtract the like components of the vectors.

Suppose we have a vector in three-dimensional space such as {eq}<a_x, a_y, a_z> {/eq}, then the sum of the square of each component is {eq}a_x^2+a_y^2+a_z^2 {/eq} and the square root of this expression will be the magnitude of the vector.

  • {eq}||a||=\sqrt{a_x^2+a_y^2+a_z^2} {/eq}

Answer and Explanation:

The given vectors in three dimensional space are:

{eq}u= \langle 3,10,9 \rangle \\ v= \langle 9,-5,7\rangle {/eq}

The magnitude of the vector...

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Learn more about this topic:

Practice Adding & Subtracting Vectors

from High School Physics: Homework Help Resource

Chapter 3 / Lesson 23

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