7. Find any two ON (orthonormal) vectors in (a) span {(1,2), (6, -1)} (b) span {(1, 2, 4), (2, -1,3)} - (c) span {(1,-1,0), (1,2,3)}

Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3]. (a) Show that the vectors u₁, u₂ and u3 are linearly independent. (b) Show that the vector v is in the span of u₁, U₂ and u3. (c) Find the coordinate vector of v with respect to {U₁, U2, U3}. (d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3 and w.

Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in xyz-space are orthogonal to v?

Plz