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4. Find the angle that the long diagonal of a 3 x 4 x 5 rectangular box makes with the longest edge.= arccos(1/4). Prove5, Suppose x, y e R", ||x ||= 2, |ly||= 1, and the angle 0 between x and y is ethat the vectors X - 3y and x + y are orthogonal.6. Suppose x, y, z e R are unit vectors satisfying x + y + z = 0. What can you say about the anglesbetween each pair?

Question

Please help me number 6. Thanks!

4. Find the angle that the long diagonal of a 3 x 4 x 5 rectangular box makes with the longest edge.
= arccos(1/4). Prove
5, Suppose x, y e R", ||x ||= 2, |ly||= 1, and the angle 0 between x and y is e
that the vectors X - 3y and x + y are orthogonal.
6. Suppose x, y, z e R are unit vectors satisfying x + y + z = 0. What can you say about the angles
between each pair?
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4. Find the angle that the long diagonal of a 3 x 4 x 5 rectangular box makes with the longest edge. = arccos(1/4). Prove 5, Suppose x, y e R", ||x ||= 2, |ly||= 1, and the angle 0 between x and y is e that the vectors X - 3y and x + y are orthogonal. 6. Suppose x, y, z e R are unit vectors satisfying x + y + z = 0. What can you say about the angles between each pair?

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Step 1

We are given that the unit vectors x, y, z satisfies the equation

To find the relation between the relation between angles of each pair we have to take dot product with x, y, z

x+y+z = 0
X-
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x+y+z = 0 X-

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Step 2

By taking the dot products we get

While taking dot product consider the fact that all vectors are unity.

xy+xz-
X.vxz=
xy+yz=-
xz+yz = -1
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xy+xz- X.vxz= xy+yz=- xz+yz = -1

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Step 3

Adding the three equations we get

From t...

3
xyyz+xz
x.y=yz=zx= -
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3 xyyz+xz x.y=yz=zx= -

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