  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 help_outlineImage Transcriptionclose4. 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? fullscreen
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

Step 2

By taking the dot products we get

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

Step 3

Adding the three equations we get

From t...

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