Find the magnitude of two vectors vec{a} and | vedclass

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(A) Let the magnitude of the vectors be $|\vec{a}| = |\vec{b}| = x$.The scalar product of two vectors is given by $\vec{a} \cdot \vec{b} = |\vec{a}| |

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the magnitude of the vectors be $|\vec{a}| = |\vec{b}| = x$.The scalar product of two vectors is given by $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$.Given that $\vec{a} \cdot \vec{b} = \frac{1}{2}$ and the angle $	heta = 60^{\circ}$.Substituting these values into the formula:$\frac{1}{2} = x \cdot x \cdot \cos(60^{\circ})$Since $\cos(60^{\circ}) = \frac{1}{2}$,we have:$\frac{1}{2} = x^2 \cdot \frac{1}{2}$Multiplying both sides by $2$:$1 = x^2$Taking the square root (since magnitude must be positive):$x = 1$Therefore,$|\vec{a}| = |\vec{b}| = 1$.

Find the magnitude of two vectors $\vec{a}$ and $\vec{b}$,having the same magnitude and such that the angle between them is $60^{\circ}$ and their scalar product is $\frac{1}{2}$.

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