Wednesday, April 4, 2012

`u = , v = ` 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 evaluate the product of the vectors u and v, such that:


`u*v = u_x*v_x + u_y*v_y`


`u*v = 1*0 + 0*(-2)`


`u*v = 0`


Hence, since `u*v = 0` , it does not matter what are the values of the magnitudes |u| and |v| since `cos theta = 0` .


`cos theta = 0 => theta = pi/2`


Hence, the angle between the vectors u and v is `pi/2` , so, the vector u is perpendicular to the vector v.

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