Question

TAKE HOME1. Find the angle between the vectors:i-23 + 5k and 3i+j - 2k

Answer 1

Answer:

The angle between the two vectors

∝ = 64°

Step-by-step explanation:

Step(i):-

Given that the vectors

                           $a^{-} = i^{-} - 2j^{-} +5k^{-}$

          and

                         $b^{-} = 3i^{-} +j^{-} -2k^{-}$

$(a^{-} . b^{-} ) = (i^{-} - 2j^{-} +5k^{-} ) . (3 i^{-} + j^{-} - 2k^{-} )$

           =  3 (i⁻ . i⁻) - 2(j⁻.j⁻) -10(k⁻.k⁻)

          = 3 - 2 -10

          = -9

Step(ii):-

Let '∝' be the angle between the two vectors

                    $cos\alpha = \frac{a^{-}.b^{-} }{|a||b|}$

                  $cos\alpha = \frac{|-9| }{\sqrt{1+4+25}\sqrt{9+1+4} }$

                 $cos\alpha = \frac{|-9| }{\sqrt{30}\sqrt{14} }$

               $\alpha =cos^{-1} ( \frac{|-9| }{\sqrt{30}\sqrt{14} })$

              ∝ = cos⁻¹(0.4392) = 63.947

Final answer:-

The angle between the two vectors

               ∝ = cos⁻¹(0.4392) = 63.947

                ∝ = 64°