# u = cos(pi/4)i + sin(pi/4)j, v = cos(pi/2)i + sin(pi/2)j Find the angle theta between the vectors.

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:

u*v = |u|*|v|*cos(theta)

The angle between the vectors u and v is theta.

cos theta = (u*v)/(|u|*|v|)

First, you need to...

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You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:

u*v = |u|*|v|*cos(theta)

The angle between the vectors u and v is theta.

cos theta = (u*v)/(|u|*|v|)

First, you need to evaluate the product of the vectors u and v, such that:

u*v = u_x*v_x + u_y*v_y

u*v = cos(pi/4)*cos(pi/2) + sin(pi/4)*sin(pi/2)

u*v = cos(pi/2-pi/4) = sin pi/4 = sqrt2/2

You need to evaluate the magnitudes |u| and |v|, such that:

|u|= sqrt(cos^2(pi/4) + sin^2(pi/4)) => |u|= sqrt(1) =>|u|= 1

|v|= sqrt(cos^2(pi/2) + sin^2(pi/2)) => |v|= sqrt(1) =>|v|= 1

cos theta = (sqrt2/2)/(1*1) => cos theta = sqrt2/2 => theta = pi/4

Hence, the cosine of the angle between the vectors u and v is cos theta = sqrt2/2 , so, theta = pi/4.

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