Q8\ 4 Points\ Let

vec(e)_(i)

denote the standard basis in

R^(n)

.\ Vectors

vec(v)

and

vec(u)

in space

R^(4)

satisfy the following conditions:\ both of them are orthogonal to

vec(e)_(3)

and

vec(e)_(4)

;\

vec(v)

is parallel to the line through

vec(e)_(1)+vec(e)_(2)

;\

vec(u)

is parallel to the line through

vec(e)_(1)+2vec(e)_(2)

;\

vec(u)+vec(v)=2vec(e)_(1)+3vec(e)_(2)

.\ Find

vec(v)

and

vec(u)

.\ Explain your answer, show your work.

Q8 4 Points Let ei denote the standard basis in Rn. Vectors v and u in space R4 satisfy the following conditions: both of them are orthogonal to e3 and e4; v is parallel to the line through e1+e2; u is parallel to the line through e1+2e2; u+v=2e1+3e2. Find v and u. Explain your answer, show your work