Q. Two vectors have magnitudes $3$ and $5 .$ If angle between them is $60^{\circ}$, then the dot product of two vectors will be:
Jharkhand CECEJharkhand CECE 2003
Solution:
The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other and multiplying it times the magnitude of the other vector. This can be expressed in the form.
$\vec{A} \cdot \vec{B}=A B \cos \theta$
$ \vec{A}$ denotes vector and $A$ denotes the magnitude of this vector.
Given, $A=3, B=5$ and $\theta=60^{\circ}$
Putting these values in above equation, we have
$\vec{A} \cdot \vec{B}=3 \times 5 \cos 60^{\circ} $
$\vec{A} \cdot \vec{B}=15 \times \frac{1}{2}=7.5$
