2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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[5]
1. Write the vector v = |3 as a linear combination of the vectors:
2. Find the distance between the given parallel planes.
2x + y+ 2z = 8 and 4x + 2y + 4z + 5 = 0
3. Find bases for the nullspace and row space of A.
1
4
6.
9
3
A =
-1
-2
1
4
-1
-1
-1
-2
7
2
8
4. Use matrix multiplication to find the image of the nonzero vector (-5,12) when it is rotated about
the origin through an angle of 0 = -60°.
5. Find two unit vectors orthogonal to both u =< 1,-1,1> and v =< 0,4,4 >.
Transcribed Image Text:[5] 1. Write the vector v = |3 as a linear combination of the vectors: 2. Find the distance between the given parallel planes. 2x + y+ 2z = 8 and 4x + 2y + 4z + 5 = 0 3. Find bases for the nullspace and row space of A. 1 4 6. 9 3 A = -1 -2 1 4 -1 -1 -1 -2 7 2 8 4. Use matrix multiplication to find the image of the nonzero vector (-5,12) when it is rotated about the origin through an angle of 0 = -60°. 5. Find two unit vectors orthogonal to both u =< 1,-1,1> and v =< 0,4,4 >.
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