   Chapter 11.4, Problem 19E

Chapter
Section
Textbook Problem

# Finding a Unit Vector In Exercises 15-18, find a unit vector that is orthogonal to both u and v. u = − 3 i + 2 j − 5 k v = i − j + 4 k

To determine

To calculate: The unit vector that is orthogonal to both the vectors u=3i+2j5k and v=ij+4k.

Explanation

Given:

The vector u and v are given as;

u=3i+2j5kv=ij+4k

Formula used:

Let, a=a1,a2,a3 and b=b1,b2,b3

Then, cross product is;

a×b=|ijka1a2a3b1b2b3|=a2b3a3b2,a3b1a1b3,a1b2a2b1

Calculation:

First, calculate the cross product of u×v as;

u×v=|ijk325114|=<

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