Question

Vector À has magnitude 10.0 m and vector B has magnitude 20.0 m. The magnitude of
the vector product |Ã Bis 100 m². What is the magnitude of the scalar product
between these two vectors?​

Answer 1

Given:

Vector A has magnitude 10.0 m and vector B has magnitude 20.0 m. Magnitude of vector product is 100 m².

To find:

Scalar product ?

Calculation:

Let angle between A and B be $\theta$:

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

$\implies 100= 10 \times 20 \times \sin( \theta)$

$\implies 100= 200 \times \sin( \theta)$

$\implies \sin( \theta) = 0.5$

$\implies \theta = {30}^{ \circ}$

Now, regarding scalar product:

$\therefore \: \vec{A}. \vec{B}$

$= A \times B \times \cos( \theta)$

$= 10 \times 20 \times \cos( {30}^{ \circ} )$

$= 10 \times 20 \times \dfrac{ \sqrt{3} }{2}$

$= 100 \sqrt{3} \: {m}^{2}$

So, scalar product is 100√3 m².