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Liquid7800

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**1.**

Hi I am writing a program to calculate 3D vectors for visualization and I am testing textbook problems such as:

Hi I am writing a program to calculate 3D vectors for visualization and I am testing textbook problems such as:

"If vector

**c**forms an obtuse angle with the 0Y-axis and is orthogonal to both vectors

**a**= 3

**i**+ 2

**j**+ 2

**k**and

**b**= 18

**i**- 22

**j**- 5

**k**

Find the components of

**c**if its norm (magnitude or length) is 14

## Homework Equations

None, just resolution of vectors by use of 3 x 3 system of equations

## The Attempt at a Solution

We know

**c**is perpendicular to

**a**AND

**b**, therefore by definition

[1] the cross product of

**a x b**is also perpendicular to

**a**AND

**b**

So we can assume that they lie in the same vector path/direction.

However they are not the same length / magnitutde so they are not the same vector

Therefore we want a vector such that the magnitude of

**c**= 14 where <c1, c2, c3> are components of

**c**.

Also by definition the dot product of two vectors will be zero if they are perpendicular to each other, so we can say:

c * a = 0

c * b = 0

c * (a x b) = 196 | 14^2 is 196

Since

**c**and a x b lie in the same path but share different magnitudes they are not the same vector...we want one along the same path that HAS a magnitude of 14...so we can create a system of equations that will produce the values of c1 , c2, and c3 as scalar multiples of

**a x b**such that the magnitude of of the equation would be 14

Therefore we would have:

3

**c1**+ 2

**c2**+ 2

**c3**= 0 |

**a**= <3,2,2>

18

**c1**- 22

**c2**-5

**c3**= 0 |

**b**= <18,-22,-5>

34

**c1**+ 51

**c2**- 102

**c3**= 14^2 (or 196) |(a x b) = <34, 51, -102>

After solving the system we would get the necessary values for <c1, c2, c3> for

**c**.

So, is this the correct way to approach such a problem or is this WAY too complex and\or unnecessary----or at worst INCORRECT?

I really appreciate any insight into this as I'd like to know if this is the most efficient WAY to solve this problem.

Thanks