solve question 4 with explanation asap and get upvotes Problem 6. (The cross product project). The cross product for vectors in V is not associative, sosome alternative way of handling expressions like a x (b x c) is sorely needed. We're going to provethe most common one here, in a few simple steps. Please review the material on the cross productin the notes ("Vectors in space", "Rotations in space", particularly the ezercises). If you use factsabout the cross product from elsewhere I will count the whole problem as 0.1. Explain why a x (b × c) must be a linear combination of b and c.2. Under what conditions is yb+ ốc perpendicular to a? What does this say about the coefficientsof b and e in the linear combination a x (b × c) = _b+ _c?3. Explain why if u and v are perpendicular, u x v = uv.4. Show how to find a vector ẽ = c – Xb that's perpendicular to b and is a linear combination ofb and c. For this vector, show that b x c = b x ẽ = bẽ.5. Conclude from this that if b x e = 0 then b is a scalar multiple of c or vice versa (b and c arelinearly dependent).6. Now, the mapping a → a x (b x c) is linear, so is determined by the image of three mutuallyperpendicular, nonzero vectors. Explain why b,ẽ and be are three mutually perpendicularnonzero vectors (assuming b x c ± 0) and then evaluate the mapping at these inputs. Why isit enough to computeb x (b x e)Can you use the quaternion product here? Why does that help?7. Parts 1 and 2 should have narrowed down the coefficients to scalar multiples of a •c and a• b.Explain. Part 5 lets you find the scalars. What is the final formula?8. The (*) is to note that we left out some "edge cases". It could be that b = 0. Is the identityyou found true in that case? it could also happen that ẽ = 0. What does that say about bx c?is the identity true in that case?

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solve question 4 with explanation asap and get upvotes Problem 6. (The cross product project). The cross product for vectors in V is not associative, sosome alternative way of handling expressions like a x (b x c) is sorely needed. We're going to provethe most common one here, in a few simple steps. Please review the material on the cross productin the notes (&#34;Vectors in space&#34;, &#34;Rotations in space&#34;, particularly the ezercises). If you use factsabout the cross product from elsewhere I will count the whole problem as 0.1. Explain why a x (b × c) must be a linear combination of b and c.2. Under what conditions is yb+ ốc perpendicular to a? What does this say about the coefficientsof b and e in the linear combination a x (b × c) = _b+ _c?3. Explain why if u and v are perpendicular, u x v = uv.4. Show how to find a vector ẽ = c – Xb that's perpendicular to b and is a linear combination ofb and c. For this vector, show that b x c = b x ẽ = bẽ.5. Conclude from this that if b x e = 0 then b is a scalar multiple of c or vice versa (b and c arelinearly dependent).6. Now, the mapping a → a x (b x c) is linear, so is determined by the image of three mutuallyperpendicular, nonzero vectors. Explain why b,ẽ and be are three mutually perpendicularnonzero vectors (assuming b x c ± 0) and then evaluate the mapping at these inputs. Why isit enough to computeb x (b x e)Can you use the quaternion product here? Why does that help?7. Parts 1 and 2 should have narrowed down the coefficients to scalar multiples of a •c and a• b.Explain. Part 5 lets you find the scalars. What is the final formula?8. The (*) is to note that we left out some &#34;edge cases&#34;. It could be that b = 0. Is the identityyou found true in that case? it could also happen that ẽ = 0. What does that say about bx c?is the identity true in that case?

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4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b and c. For this vector, show that b x c = b x ē = bē.