How do I find two vectors that are orthogonal to each other?

[nickerst]

1. Find a nonzero vector v in span {v2,v3} such that v is orthogonal to v3. Express v as a linear combination of v2 and v3


2. v1= [3 5 11] v2= [5 9 20] v3= [11 20 49]


3. I know that the dot product of v and v3 must equal zero. And that v must have components between 5 and 11, 9 and 20, and 20 and 49. But I can't find the solution. I tried using pythagoras' theorem for vectors, as well as orthogonal projections but both don't work.

 

[LCKurtz]

What does v1 have to do with the question? Do you know how to find the vector projection of v2 on v3? If so, you can just subtract it from v2 to get the orthogonal projection vector.

 

[nickerst]

LCKurtz What does v1 have to do with the question? Do you know how to find the vector projection of v2 on v3? If so, you can just subtract it from v2 to get the orthogonal projection vector.

I suppose v1 doesn't have anything to do with the question.

Is the vector projection of v2 onto v3 = [(v2 dot v3) / Length(v3) squared] times v3? If so I then just subtract it from v2 and that's my answer?

 

[nickerst]

Thank you very much LCKurtz! It worked!