# Orthogonal Vectors in R3

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#1
Hey everyone, struggling a bit with my reasonings for this question:

Let v1 and v2 be two linearly independent vectors in R3.

Say how many vectors of norm 5 exist in R3 that are orthogonal to both v1 and v2. Justify your answer.

Find one such vector when v1=(1,0,1) and v2=(0,-6,2)

Denote by v3 the vector found in part 2, show that f={v1,v2,v3} is a basis for R3 and find the change of basis matrix to the standard basis e={e1,e2,e3} of R3 to f.

Help on any of the sections would be lovely.

Thanks
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6 years ago
#2
(Original post by DanSheath)
Hey everyone, struggling a bit with my reasonings for this question:

Let v1 and v2 be two linearly independent vectors in R3.

Say how many vectors of norm 5 exist in R3 that are orthogonal to both v1 and v2. Justify your answer.

Find one such vector when v1=(1,0,1) and v2=(0,-6,2)

Denote by v3 the vector found in part 2, show that f={v1,v2,v3} is a basis for R3 and find the change of basis matrix to the standard basis e={e1,e2,e3} of R3 to f.

Help on any of the sections would be lovely.

Thanks
Visualise what it means for a vector to be orthogonal in three-dimensional space. Then each vector that meets your criteria must have a norm of 5.
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