(a) Find the cosine of the angle between the lines L1 and L2 whose vector equations are given below:
L1 : ~r1(t) = [1, 1, 1] + t[1, 2, 3]
L2 : ~r2(t) = [1, 1, 1] + t[−1, 4, 2].
(b) Find the equation of the plane that contains both L1 and L2.
Given two sorted lists, L1 and L2, write an efficient C++ code
to compute L1 ∩ L2 using only the basic STL list operations. What
is the running time of your algorithm?
1. Write a Racket function (set-equal? L1 L2) that tests whether
L1 and L2 are equal. Two sets are equal if they contain exactly the
same members, ignoring ordering (or in other words, two sets are
equal if they are a subset of each other).
For example (set-equal? '(1 (2 3)) '((3 2) 1)) ---> #t
(set-equal? '(1 2 3) '((3 2)1)) ---> #f
(set-equal? '(1 2 3) '((1 2 3))) ---> #f
2. Two common operations on sets are...
Recall that given a line L1 in the plane with slope m, a second
line L2 is perpendicular to L1 if and only if the slope of L2 is −
1 m . Now consider the function h(x) = x^2 + 3/2x + 3. Among all of
the lines tangent to the graph of h(x), there is exactly one which
is perpendicular to the line given by y = −2x + 7. Write the
equation of that line tangent to...
Find the distance between the skew lines with parametric
equations x = 1 + t, y = 3 +
6t, z = 2t, and
x = 1 + 2s, y = 6 + 15s, z
= −2 + 6s.
Find the equation of the line that passes through the points on
the two lines where the shortest distance is measured.
ABC ltd is a circuit board producer and produces two products,
L1 & L2. The company currently uses traditional costing system
for making business decisions. However, recently the company is
considering a move towards the Activity-Based Costing (ABC) system.
As one of the company’s accountant’s you have been asked to prepare
a statement comparing both the costing methods for the next company
board meeting. Your supervisor has given you the following
quarterly data: -
Total Indirect Costs for the quarter:...