(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a unit vector which is perpendicular to both of the vectors a = 4i + 2j - 3k and b = 2i - 3j + k

c = xi + yj + zk

2. Relevant equations

a[tex]\bot[/tex]c [tex]\longrightarrow[/tex] a [tex]\bullet[/tex] c

3. The attempt at a solution

Okay, here's what I've done so far.

Take the dot-product of a and c, and b and c

a [tex]\bullet[/tex]b: 4x + 2y -3z = 0

b [tex]\bullet[/tex]b: 2x - 3y + z = 0

(1) 4x + 2y -3z = 0

(2) 2x - 3y + z = 0

I isolate z and get rid of x by multiplying (1) with -2 and (2) with 4, then add them:

(1) -8x -4y = -6z

+

(2) 8x -12y = 5z

-16y = 10z

y/z = 10/16

Which again means that:

y = 10m

z = 16m

where m is a constant and [tex]\neq[/tex] 0

And then I insert this into (1) to find x:

4x + 2(10m) - 3(16m) = 0

4x + 20m - 48m = 0

x = 7m

c = m(7i + 10j + 16k)

For the easiest possible solution, m = 1.

c = 7i + 10j + 16k

As far as I can tell, this is a perfectly valid answer.

However, the answer key has the answer:

(1/9[tex]\sqrt{5}[/tex])(7i + 10j + 16k)

While this does not contradict my solution, that is a far too weird m to have been chosen randomly. Does anyone see how they were thinking?

Thanks

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Unit vector perpendicular to two known vectors

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