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.
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