Question

p=2i+j and q=5i+3j find the cosine of angle between a and b​

Answer 1

Answer:

$\cos( \alpha ) = \frac{13}{ \sqrt{170} }$

Step-by-step explanation:

Using the dot product,

$p.q = |p| |q| \cos( \alpha )$

Where alpha is angle between the vectors,

$(2i + j).(5i + 3j) = \sqrt{ ({2}^{2} + {1}^{2} )} \times \sqrt{( {5}^{2} + {3}^{2} ) } \cos( \alpha )$

$10 + 3 = \sqrt{5} \times \sqrt{34} \cos( \alpha )$

$\cos( \alpha ) = \frac{13}{ \sqrt{170} }$