Question

find the angle between a diagonal of a cube and an adjacent edge. (enter your answer in degrees. round your answer to two decimal places.)

Answer 1

The angle between a diagonal of a cube and an adjacent edge is 54.75°;

Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;

a = (1, 0, 0)

b = (0, 1, 0)

c = (0, 0, 1)

The diagonal is given by the vector, v = (1, 1, 1)

The angle between the diagonal and one edge of the cube is given by

cos θ = v. a / |v|.|a|

v. a = (1, 1, 1).(1, 0, 0)

= 1(1) + 1(0) + 1(0

= 1 + 0 + 0

v. a = 1

Magnitude of vector V = √[(1)² + (1)² + (1)²]

|v| = √3

Similarly, |a| = √1;

So, |v|.|a| = √3.√1 = √3

Now, cos θ = 1/√3

So, θ = cos¹(1/√3)

θ = 54.75°

Therefore, the required angle is 54.75°.

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