Find the shortest distance from the origin to the line of intersection of the planes 2 x − 3 y + z = 5 , 3 x − y − 2 z = 11 , (a) using vector methods (see Chapter 3, Section 5 ); (b) using Lagrange multipliers.
Find the shortest distance from the origin to the line of intersection of the planes 2 x − 3 y + z = 5 , 3 x − y − 2 z = 11 , (a) using vector methods (see Chapter 3, Section 5 ); (b) using Lagrange multipliers.
Find the shortest distance from the origin to the line of intersection of the planes
2
x
−
3
y
+
z
=
5
,
3
x
−
y
−
2
z
=
11
,
(a) using vector methods (see Chapter 3, Section 5 );
(b) using Lagrange multipliers.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows:P1=(10,15), P2=(20,25) ve P3=(40,5)To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the2two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively.Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move simultaneously in both directions.…
B) The line passes through the point (2,4,5) and perpendicular to the plane 2x+y-5z-21,
intersects the x-y plane at the point P₁. Use Lagrange multiplier to find the shortest distance
between P, and the plane x+2y-z-1.
Mathematics for Elementary Teachers with Activities (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.