If theta is the angle between any two vectors | vedclass

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Question

(A) Let $	heta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$.Assuming $\vec{a}$ and $\vec{b}$ are non-zero vectors,we have $|\vec{a}| > 0

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(A) Let $	heta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$.Assuming $\vec{a}$ and $\vec{b}$ are non-zero vectors,we have $|\vec{a}| > 0$ and $|\vec{b}| > 0$.The given condition is $|\vec{a} \cdot \vec{b}| = |\vec{a} 	imes \vec{b}|$.Using the definitions of dot and cross products,we get $|\vec{a}||\vec{b}| |\cos 	heta| = |\vec{a}||\vec{b}| |\sin 	heta|$.Since $|\vec{a}|$ and $|\vec{b}|$ are positive,we can divide both sides by $|\vec{a}||\vec{b}|$,yielding $|\cos 	heta| = |\sin 	heta|$.This implies $|	an 	heta| = 1$.For $	heta$ in the range $[0, \pi]$,$	an 	heta = 1$ gives $	heta = \frac{\pi}{4}$.Thus,the condition holds when $	heta = \frac{\pi}{4}$.The correct answer is $A$.

If $\theta$ is the angle between any two vectors $\vec{a}$ and $\vec{b},$ then $|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|$ when $\theta$ is equal to

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