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# GivenavectorbR3,letU={xR3 :bx=0}. (Here denotes the cross product of two vectors.) i) Prove that U is a subspace of R3. 1 ii) If b = 2 , write down a...

Givenavectorb∈R3,letU={x∈R3 :b×x=0}.

(Here × denotes the cross product of two vectors.) i) Prove that U is a subspace of R3.

−1 ii) If b = 2 , write down a basis for U, giving reasons.

3