If the angle between the vectors a and b is t | vedclass

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Question

(D) The scalar product (dot product) of two vectors $a$ and $b$ is defined as $a \cdot b = |a| |b| \cos 	heta$. Given that $a \cdot b = \cos 	heta$.

Vedclass · Accepted Answer

$a$ and $b$ are unit vectors

Vedclass · Answer

(D) The scalar product (dot product) of two vectors $a$ and $b$ is defined as $a \cdot b = |a| |b| \cos 	heta$. Given that $a \cdot b = \cos 	heta$. Comparing the two expressions,we have $|a| |b| \cos 	heta = \cos 	heta$. This implies $|a| |b| = 1$. Since the magnitude of a vector is non-negative,and for the dot product definition to hold in this specific form,it implies that the magnitudes of both vectors must be $1$. Thus,$|a| = 1$ and $|b| = 1$. Therefore,$a$ and $b$ are unit vectors.

If the angle between the vectors $a$ and $b$ is $\theta$ and $a \cdot b = \cos \theta$,then the true statement is:

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