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(a) Find the vector equations of the line through P(2,-1,4){“version”:”1.1″,”math”:”P(2,-1,4)”} and Q(1,1,-1){“version”:”1.1″,”math”:”Q(1,1,-1)”}. (b) Find the equation of the plane passing through the points P, Q{“version”:”1.1″,”math”:”P, Q”} and R(-4, 1,1 ){“version”:”1.1″,”math”:”R(-4, 1,1 )”}. (You do not need to type your answers in the space below. However, you must upload a file of your handwritten work in the final question.

Answer the following questions.  (a) Use the points P(3,1){“version”:”1.1″,”math”:”P(3,1)”} and Q(7,1){“version”:”1.1″,”math”:”Q(7,1)”} to find the vector PQ⇀{“version”:”1.1″,”math”:”PQ⇀”}. (b) Find the magnitude of the vector PQ⇀{“version”:”1.1″,”math”:”PQ⇀”}. (c) Find the unit vector of QP⇀{“version”:”1.1″,”math”:”QP⇀”}. (Caution: PQ⇀≠QP⇀{“version”:”1.1″,”math”:”PQ⇀≠QP⇀”}) (d) Express PQ⇀{“version”:”1.1″,”math”:”PQ⇀”} as the product of its magnitude and a unit vector. (You do not need to type your answers in the space below. However, you must upload a file of your handwritten work in the final question.)

Consider the following vectors u⇀= & v⇀={“version”:”1.1″,”math”:”u⇀=<4,3,0> & v⇀=<1,1,1>”}. Express u⇀{“version”:”1.1″,”math”:”u⇀”} as the sum u⇀=p⇀+n⇀{“version”:”1.1″,”math”:”u⇀=p⇀+n⇀”} , where p⇀{“version”:”1.1″,”math”:”p⇀”} is parallel to v⇀{“version”:”1.1″,”math”:”v⇀”} and n⇀{“version”:”1.1″,”math”:”n⇀”} is orthogonal to v⇀{“version”:”1.1″,”math”:”v⇀”}. (You do not need to type your answers in the space below. However, you must upload a file of your handwritten work in the final question.)

In the cytoplasm, materials are organized, separated, and sorted by membranes. Cells exploit the selective permeability of these membranes to partition populations of molecules and generate chemical energy for the cell. Use the principles of the first and second laws of thermodynamics to explain how membranes can be used to produce chemical energy.

Cell membranes are fluid, and thus proteins can diffuse laterally within the lipid bilayer. However, sometimes the cell needs to localize proteins to a particular membrane domain. Name three mechanisms that a cell can use to restrict a protein to a particular place in the cell membrane.

Sequential pathways can help drive unfavorable reactions by siphoning off the products into the next energetically favorable reaction in the series.

Complete the sentence with the best option provided below. The secondary structures of a protein are the

Which of the following is FALSE with regards to phosphorylation of proteins?

The highly ordered structure of the lipid bilayer makes its generation and maintenance energetically unfavorable.

What is responsible for protein folding at the secondary level?