Question

Find the angle between the two vectors A = 2i + 3j -k and B = i -2j + 3k.






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Answer 1

Given ,

The two vectors are

• A = 2i + 3j - k
• B = i - 2j + 3k

We know that , the angle between two vectors " x " and " y " is given by

$\boxed{ \sf \cos( \theta) = \frac{x.y}{ |x| |y| } }$

Thus ,

$\tt \cos( \theta) = \frac{2(1) + 3( - 2) + ( - 1)(3)}{ \sqrt{ {(2)}^{2} + {(3)}^{2} + {( - 1)}^{2} } \sqrt{ {(1)}^{2} + {( - 2)}^{2} + {(3)}^{2} } }$

$\tt \cos( \theta) = \frac{2 - 6 - 3}{ \sqrt{14} \sqrt{14} }$

$\tt \cos( \theta) = \frac{ - 7}{14}$

$\tt \cos( \theta) = - \frac{1}{2}$

$\tt \theta = \pi - \frac{\pi}{3}$

$\tt \theta = \frac{2 \pi}{3}$

∴ The angle between two vectors A and B is 60