Question

If (vector) |A|=2 and (vector) |B|=5 and |A×B|=8, then what is A.B equal to?

Answer 1

Hello mate ,
Given:

|A|=2

|B|=5

|A×B|=8

We know that ,

|A×B|=|A||B|sinθ

So, 2×5×sinθ=8

⟹sinθ=45

⟹cosθ=35

To evaluate:

A⋅B=|A||B|cosθ

⟹A⋅B=2×5×35

⟹A⋅B=6

Hope that you will understand it.
pls mark it as brainleast answer.

Answer 2

$A{\cdot} B=6$

Explanation:

Given that,

Vector A, $|A|=2$

Vector B, $|B|=5$

$A\times B=8$

The cross product of two vectors is given by the formula as :

$A\times B=|A||B|\ sin\theta$

$sin\theta=\dfrac{A\times B}{|A||B|}$

$sin\theta=\dfrac{8}{2\times 5}$

$sin\theta=0.8$

$\theta=53.13^{\circ}$

So, $cos\theta=0.6$

Now using dot product formula. So,

$A{\cdot}B=|A||B|\ cos\theta$

$A{\cdot}B=(2)(5)(0.6)$

$A{\cdot} B=6$

So, A.B is 6. Hence, this is the required solution.

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