The component of a vector vec{A} along a dire | vedclass

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(A) The component of a vector $\vec{A}$ along a direction making an angle $	heta$ with it is $A_	heta = A \cos 	heta$. Since the range of the cosin

Vedclass · Accepted Answer

Always less than or equal to its magnitude

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(A) The component of a vector $\vec{A}$ along a direction making an angle $	heta$ with it is $A_	heta = A \cos 	heta$. Since the range of the cosine function is $-1 \le \cos 	heta \le 1$,the magnitude of the component is $|A \cos 	heta| = |A| |\cos 	heta|$. Because $|\cos 	heta| \le 1$,it follows that $|A \cos 	heta| \le |A|$. Therefore,the component of a vector along any direction is always less than or equal to its magnitude.

The component of a vector $\vec{A}$ along a direction making an angle $\theta$ with it is given by $A \cos \theta$. What can be said about the magnitude of this component?

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