Question

what is the answer to this question

Answer 1

Hey There!

Here, we are given two vectors $\vec{A}$ and $\vec{B}$ , and the angle between them is given as $\theta$


Now, $\hat{A}$ and $\hat{B}$ represent Unit Vectors in the direction of $\vec{A}$ and $\vec{B}$ respectively.


Unit Vectors have a specific direction, but their magnitude is 1 

That is:

$| \hat{A} | = 1 \\ \\ | \hat{B} | = 1$


The angle between these two vectors is also $\theta$


Now, cross product is defined as :

$\hat{A} \times \hat{B} = |\hat{A} | \, |\hat{B} | \, \sin \theta \\ \\ \\ \implies \hat{A} \times \hat{B} = (1)(1) \, \sin \theta \\ \\ \\ \implies \boxed{|\hat{A} \times \hat{B} | = \sin \theta}$


Thus, the answer is OPTION A.


Hope it helps
Purva
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