Question

) Vectors Ā and B each have magnitude L. When drawn with their tails at the same
point, the angle between them is 30°. The value of A.B is:

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Answer 1

We have to take dot product of A and B

A.B = ABcosΘ

A=B =L

Θ=30°

Therefore , ABcosΘ= L²COS 30°

                                =   $L^{2} \frac{\sqrt{3} }{2}$

Answer 2

Given:

Vectors A and B are aligned at 30°.

To find:

Value of dot product ?

Calculation:

The value of Scalar/Dot product is :

$\vec{A}. \vec{B} = |A || B| \times \cos( \theta)$

• $\theta$ is angle between A and B.

$\implies \vec{A}. \vec{B} = L \times L\times \cos( {30}^{ \circ} )$

$\implies \vec{A}. \vec{B} = L \times L\times \dfrac{ \sqrt{3} }{2}$

$\implies \vec{A}. \vec{B} =\dfrac{ \sqrt{3} {L}^{2} }{2}$

So, the value of dot product is L²√3/2.