If the Cartesian equation of the line is   then direction vector of the line is

The coordinates of the point on the z-axis are of the form

The center of a sphere is  , one endpoint of the diameter is then the another endpoint is

Which of the following is the correct inductive step for proving the formula  for all natural numbers n ?

Using mathematical induction, prove 7ⁿ – 1 is divisible by 6 for all natural numbers n. What is the induction hypothesis?

In the inductive step of a proof, what assumption is made?

Which of the following is a valid form of the inductive hypothesis when using induction to prove  is divisible by 8 for all natural numbers n?

For proving for large natural number n, what should the inductive step be?

The value of Im (i²⁶) =

If z = 3 – 4i, then