How do I find the projection of the normal vector of the plane $$2x+y+z=4$$ onto a unit direction vector field for the line $$x=1-t, \quad y=1+2t, \quad z=2-3t\,?$$
Projection of the normal vector of the plane
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$\begingroup$
plane-geometry
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0Welcome to Math.SE. Which part are you stuck on? Do you know how to find a normal vector of the plane? Do you know how to find a unit direction vector for the line? Do you know how to project a vector onto a subspace? – 2017-01-09
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0@MyGlasses Perhaps you meant in your last line "the direction vector is...", because it may well be $\;(a,b,c)\;$ isn't a unit a vector. – 2017-01-09
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0@DonAntonio Sorry. yes – 2017-01-09
1 Answers
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Hint:
The normal vector to the plane is $\vec v=(2,1,1)^T$.
The direction vector of the line is $\vec u=(-1,2,-3)^T$
Do you see this?
Now use the inner product to find the projection of one vector on the on the direction of the other.
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0sorry mate what is the meaning of )T ? – 2017-01-09
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0Simply the symbol of ''transpose'', used to indicate that the vector is, as usual, a column vector. (But really you can think also at a row vector). – 2017-01-09