Determine the angle 0 between the sides of the triangular plate. Given: i = lm b...

Question

Question

Answer 1

Answer #1

We have the following points: A(0, 1, 1), B(0, 3, 4) and C(3, 5, 0)

Now,

vector AB = (0 - 0) i + (3 - 1) j + (4 - 1) k = 2 j + 3 k

vector AC = (3 - 0) i + (5 - 1) j + (0 - 1) k = 3 i + 4 j - k

Using the dot product of vectors AB and AC, we get,

cosθ = AB.AC / (|AB| |AC|) = (2 j + 3 k).(3 i + 4 j - k) / [(2² + 3²)^1/2 (3² + 4² + (-1)²)^1/2] = 5 / (13 * 2^1/2)

=> θ = cos^-1[5 / (13 * 2^1/2)] = 74.2^o

Answer 2

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