Which of the following is not a unit vector f | vedclass

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(C) vector $\vec{v} = x\,i + y\,j$ is a unit vector if its magnitude $|\vec{v}| = \sqrt{x^2 + y^2} = 1$,which implies $x^2 + y^2 = 1$.For option $A$:

Vedclass · Accepted Answer

$(\sin 2	heta )\,i - (\cos 	heta )\,j$

Vedclass · Answer

(C) vector $\vec{v} = x\,i + y\,j$ is a unit vector if its magnitude $|\vec{v}| = \sqrt{x^2 + y^2} = 1$,which implies $x^2 + y^2 = 1$.For option $A$: $(\cos 	heta)^2 + (-\sin 	heta)^2 = \cos^2 	heta + \sin^2 	heta = 1$.For option $B$: $(\sin 	heta)^2 + (\cos 	heta)^2 = \sin^2 	heta + \cos^2 	heta = 1$.For option $C$: $(\sin 2	heta)^2 + (-\cos 	heta)^2 = \sin^2 2	heta + \cos^2 	heta$. This is not equal to $1$ for all values of $	heta$ (e.g.,at $	heta = \frac{\pi}{4}$,$\sin^2(\frac{\pi}{2}) + \cos^2(\frac{\pi}{4}) = 1^2 + (\frac{1}{\sqrt{2}})^2 = 1 + 0.5 = 1.5 
eq 1$).For option $D$: $(\cos 2	heta)^2 + (-\sin 2	heta)^2 = \cos^2 2	heta + \sin^2 2	heta = 1$.Therefore,the vector in option $C$ is not a unit vector for all values of $	heta$.

Which of the following is not a unit vector for all values of $\theta$?

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