Introductory linear algebra: Let L be the line with the parametric equations x=2+t ; y=1-t ; z= 1+3t and let v= . Find vectors w1 and w2 such that v=w1+w2 and such that w1 is parallel to L and w2 is perpendicular to L.

Question

Introductory linear algebra:

Let L be the line with the parametric equations x=2+t ; y=1-t ; z= 1+3t and let v= <1,2,0>. Find vectors w1 and w2 such that v=w1+w2 and such that w1 is parallel to L and w2 is perpendicular to L.

amistre64 · Answer

parallel vectors are the same vector ... so w1 is equal to the direction vector of the given line

anonymous · Answer

I know that the direction vector <1,-1,3> is parallel to the line L. I just can't seem to find a w2 value that is orthogonal to L and satisfies the equation. ie) w1 = <1,-1,3> v= <1,2,0> and w2 would give me <0,3,-3>, which isnt orthogonal to w1

amistre64 · Answer

consider the projection of v onto L

amistre64 · Answer

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anonymous · Answer

ok ill try that

amistre64 · Answer

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