`u = 2i - 3j, v = 4i + 3j` Find the angle theta between the vectors.

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We want to get the angle,  between vectors u = 2i -3j and v = 4i + 3j. By definition, the angle  between two vectors is defined as follows (u and v are two vectors):

 .Hence,  .

`||u|| = \sqrt(2^2+(-3)^2) = \sqrt(13)` .

`||v|| = \sqrt(4^2)+(3^2) = \sqrt(25) = 5`  .

`u \cdot v...

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We want to get the angle,  between vectors u = 2i -3j and v = 4i + 3j. By definition, the angle  between two vectors is defined as follows (u and v are two vectors):

 .Hence,  .

`||u|| = \sqrt(2^2+(-3)^2) = \sqrt(13)` .

`||v|| = \sqrt(4^2)+(3^2) = \sqrt(25) = 5`  .

`u \cdot v = 2*4 + (3*-3) = -1`  .

Hence, `\theta = cos^(-1) (-1)/(\sqrt(13)*5) = -(\sqrt(13))/(65) \approx 1.63`  .

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