Let a⃗ =2i^+2j^+k^𝑎→=2𝑖^+2𝑗^+𝑘^ and b⃗ 𝑏→ be another vector such that a⃗ .b⃗ =14𝑎→.𝑏→=14 and a⃗ ×b⃗ =3i^+j^−8k^𝑎→×𝑏→=3𝑖^+𝑗^−8𝑘^ the vector b⃗ 𝑏→ =

Let a⃗ =2i^+2j^+k^𝑎→=2𝑖^+2𝑗^+𝑘^ and b⃗ 𝑏→ be another vector such that a⃗ .b⃗ =14𝑎→.𝑏→=14 and a⃗ ×b⃗ =3i^+j^−8k^𝑎→×𝑏→=3𝑖^+𝑗^−8𝑘^ the vector b⃗ 𝑏→ =

Find the angle between the following two vectors:a⃗ =⟨0,−5⟩𝑎→=⟨0,−5⟩ and b⃗ =⟨1,−4⟩𝑏→=⟨1,−4⟩(Round your answer to the nearest whole degree.)

Find a unit vector for a⃗ =<1,7>𝑎→=<1,7> in component form.Your final answer should have the denominator rationalized.

The position vector of the point (1, 2, 0) is....Ai + j +kBi + 2j + kCi + 2jD2j + k

Let 𝑄∗ be the set of non-zero rational numbers and * be the binary operation on Q definedby 𝑎 ∗ 𝑏 = 𝑎𝑏/3. Prove that 𝑄∗ is group under *.