Answer:
The angle between the two vectors
∝ = 64°
Step-by-step explanation:
Step(i):-
Given that the vectors
[tex]a^{-} = i^{-} - 2j^{-} +5k^{-}[/tex]
and
[tex]b^{-} = 3i^{-} +j^{-} -2k^{-}[/tex]
[tex](a^{-} . b^{-} ) = (i^{-} - 2j^{-} +5k^{-} ) . (3 i^{-} + j^{-} - 2k^{-} )[/tex]
= 3 (i⁻ . i⁻) - 2(j⁻.j⁻) -10(k⁻.k⁻)
= 3 - 2 -10
= -9
Step(ii):-
Let '∝' be the angle between the two vectors
[tex]cos\alpha = \frac{a^{-}.b^{-} }{|a||b|}[/tex]
[tex]cos\alpha = \frac{|-9| }{\sqrt{1+4+25}\sqrt{9+1+4} }[/tex]
[tex]cos\alpha = \frac{|-9| }{\sqrt{30}\sqrt{14} }[/tex]
[tex]\alpha =cos^{-1} ( \frac{|-9| }{\sqrt{30}\sqrt{14} })[/tex]
∝ = cos⁻¹(0.4392) = 63.947
Final answer:-
The angle between the two vectors
∝ = cos⁻¹(0.4392) = 63.947
∝ = 64°
