3. Vectors A and B are applied at the origin. A-3/ +j B = i + 4j what is the ang

Question

3. Vectors A and B are applied at the origin. A-3/ +j B = i + 4j what is the angle, , between A and B? Report your answer to the nearest tenth of a degree. a. Design a function such that when two vectors A and B (defined as two 1 x 2 matrices) are used as the input and the output is the angle in degrees between A and B. Input. A = [A. A], B= [B, BI Output: angle in degrees between A and B Solve the above problem using a graph and your calculator, then plug the problem into your Matab function and compare results.

Explanation / Answer

The dot product of A and B

ABcos(x) = -3*1 + 1*4

sqrt((3*3 + 1)(1 + 4*4))*cos(x) = 1

cos(x) = 1 / sqrt(170)

x = acos(1/sqrt(170))

x = 85.6degrees

The corresponding function in MATLAB is defined as follows

function theta = angle(A ,B)
d = dot(A, B);
c = sqrt(sum(A.^2) * sum(B.^2));
theta = acos(d / c) * 180 / acos(-1);
end

a = [-3 1];

b = [1 4];

angle(a,b)

ans = 85.601

Best regards

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