Find the distance between the two parallel planes- find the

Question

Question 1. Use induction to prove: for all n = 1, 2, 3, ......

Question 2. Show that ∏^Π_r=2(1 -1/r²) = (n+1)/2n  for all n = 1, 2, 3....

Question 3. show n⁷/7 + n³/3 + 11n/21 is an integer all n.

Question 4. Let P(n) be the statement: "n²+n+1 is even." Show that P(n) ⇒ P(n +1)

Question 5. If a = < 1, 2, 3 >  b = < 0, 1,-1 > and c = < 2, 1, 0 >

Find: a.b         a.c        b.c

       axb         bxc       axc

       a.bxc      axb.c     ax(bxc) & (axb)xc

 Find the angle between a & b, between axb & c, between axb & bxc.

Question 6. Find the distance between the two (parallel) planes: x + y - z = 0 & x + y - z = 5.

Question 7. Find the point of intersection of the three planes:

x + y + z = 2

x - y + z = -2

2x + y - z = 5

Question 8. Find the (shortest) distance from the point (1, 2, 3) to the plane: x + y - z - 5 = 0