`u = 2i - j ,v = 6i + 4j` Find the angle theta between the vectors.

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The angle between two vectors u and v is given by;

`costheta = (u.v)/(|u||v|)`

u.v represent the vector dot product and |u| and |v| represents the magnitude of vectors.

We know that in unit vectors;

`ixxi = jxxj = 1` and `ixxj = jxxi = 0`

`u =...

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The angle between two vectors u and v is given by;

`costheta = (u.v)/(|u||v|)`

 

u.v represent the vector dot product and |u| and |v| represents the magnitude of vectors.

We know that in unit vectors;

`ixxi = jxxj = 1` and `ixxj = jxxi = 0`

 

`u = 2i-j`

`v = 6i+4j`

 

`u.v = 2xx6-1xx4 = 8`

 

The magnitude of the vectors is given by;

`|u| = sqrt(2^2+(-1)^2) = sqrt5`

`|v| = sqrt(6^2+4^2) = sqrt52`

 

`costheta = 8/(sqrt5xxsqrt52)`

`theta = cos^(-1)(8/sqrt260)`

`theta = 60.255 deg`

 

So the angle theta between two vectors  is 60.255 deg

 

 

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