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Homework Statement
From Kleppner and Kolenkow Chapter 1 (Just checking to see if I'm right)
Given vector A=<3, 4, -4>
a) Find a unit vector B that lies in the x-y plane and is perpendicular to A.
b) Find a unit vector C that is perpendicular to both A and B.
c)Show that A is perpendicular to the plane defined by B and C.
Homework Equations
Cross Product
Dot Product
Knowing how to find a plane from two vectors
The Attempt at a Solution
a) Using the following system...
3x+4y=0 (using dot product and z=0)
x+y=1 (For it to be a unit vector the sum of the two components must be 1)
The perendicular vector is
##<4, -3, 0>##
and the unit vector after dividing by the magnitude is...
##B=<4/5, -3/5, 0>##
b)Finding the cross product of A and B and dividing by the magnitude...
##C=<\frac{-12,}{5\sqrt{41}}, \frac{-16}{5\sqrt{41}}, \frac{-5}{\sqrt{41}}>##
c)##B \times C=<75, 100, -100>##
Therefore the plane is defined by...
##3x+4y-4z=0##
Therefore A is perpendicular since its components equal the constants that define the plane.
I'm pretty sure I did everything right I just wanted to make sure and see if any of my wording is dumb or if I made a mistake. I don't know how to write the last part formally. Thanks all!