`u = -6i - 3j, v = -8i + 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 = -6i-3j`

`v = -8i+4j`

 

`u.v = (-6)xx(-8)+(-3)xx4 = 36`

 

`|u| = sqrt((-6)^2+(-3)^2) = sqrt(45)`

`|v| = sqrt((-8)^2+4^2) = sqrt80`

 

The angle between vectors is given by;

`costheta = 36/((sqrt45)(sqrt80))`

`theta = cos^(-1)(36/sqrt(3600))`

`theta = 53.13 deg`

 

So the angle between two vectors is 53.13 deg

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