Please see the attached file for the fully formatted problems.

Problems involve:
parametric equation of line segment,
volume of a parallelipiped,
sketching a plane gven the equation,
finding rectangular equations,
center and radius of a sphere using the equation of a sphere,
force vector problems.

1.)
The important points are: intersection of plane with 3 axes x, y, z.
x+2y+4z = 8
Interception on x axis: y=0,z=0, x = 8
Interception with y axis: x=0,z=0, y = 4
Interception with zaxis: x=0,y=0, z = 2
therefore,
three well known points are: (8,0,0), (0,4,0), (0,0,2)
See the attached file.

2.)
P(2,-1,4), Q(5,3,3)
x1-x2 = 2 - 5 = -3
y1-y2 = -1 - 3 = -4
z1-z2 = 4 - 3 = 1
therefore direction ratios of the line given as:
a:b:c = -3:-4:1
hence the parametric equation of straight line is given as:
x = x1 + a*r
y = y1 + b*r
z = z1 + c*r
=> (x = 2 - 3r, y = -1 - 4r, z = 4 + r) --Answer

3.)
postion vectors of P,Q,R:
P = (1,-1,2)=> vector OP = v(OP) = i - j + 2k
Q = (4,1,3) => v(OQ) = 4i + j + 3k
R = (-1,1,-1) => v(OR) = -i + j - k
v(PQ) = v(OQ) - v(OP) = 3i + 2j + k
v(RQ) = v(OQ) - v(OR) = 5i + 0.j + 4k
direction cosines of the normal to the plane:
normal vector to the plane = v(n)
v(n) = v(PQ) X v(RQ) = 8i - 7j - 10k
therefore, equation of the plane:
{v(r) - v(OP)}.v(n) = 0
because, r vector - OP vector will be in the plane and dot product ...

... c) (10 pts) What is the corresponding average ... QSO 510 Quantitative Analysis Differential Calculus HW Set ... doing this assignment, work on the practice problems. ...

... Area = 10 * 10 = 100 units^2. 5. By definition: ... This solution shows you step by step on how to solve calculus problems involving differentiation. ...

Calculus Problems : Continuity, Limits, Derivatives, Inequalities, Quadratic Equations and Parabolas and Maximum ... function f(x)= 1/x+1 on the interval [-10, 10]. ...

Related Rates and calculus problems for real life situations. ... Related Rates Problems 1. A tiger escapes from a truck, right ... can only drink at a rate of 10 ml/sec ...

Calculus: Related rates problem using a ... Its length is supposed to be x = 50 meters, the width is supposed to be y = 30 meters, and the height is 10 meters ...

... Integration questions for probability and calculus are provided ... my real problem is with the integration of the problem. ... ¾ } , C2 = {1/2}, C3 = {x: 0 < x < 10}. ...

... This might fall into linear programming more than calculus. ... Stage A: Clarify the Problem. ... He will study 10 hours a week for science and social science courses ...

... Homework problem 2 A landscape supply company packages three different soil mixes sold in 20 ... Mix B contains 10 pounds of peat, 6 pounds of perlite, and 4 pounds ...

... key concepts and techniques to solve any related problems. The solution assists with answering calculus questions some ... 1) Make a List of 10 Mathish words or ...