Multiplication Of Vectors MCQ - Practice Questions with Answers

1. If a vector is multiplied by any scalar

$\vec{Z}=n \cdot \vec{Y}$

 (n=1,2,3..) 

Vector Scalar Vector

We get again a vector.

2. If a vector is multiplied by any real number (eg 2 or -2)  then again, we get a vector quantity.

    E.g.

If $\vec{A}$ is multiplied by 2 then the direction of the resultant vector is the same as that of the given vector.

$$
\text { Vector }=2 \vec{A}
$$

If $\vec{A}$ is multiplied by ( -2 ), then the direction of the resultant is opposite to that of a given vector.

$$
\text { Vector }=-2 \vec{A}
$$
 

Scalar  or Dot or Inner Product

• Scalar product of two vectors $\vec{A} \& \vec{B}$ written as $\vec{A} \cdot \vec{B}$
• $\vec{A}, \vec{B}$ is a scalar quantity given by the product of the magnitude of $\vec{A} \& \vec{B}$ and the cosine of the smaller angle between them.

$
\vec{A} \cdot \vec{B}=A B \cdot \cos \Theta
$

       Figure showing a representation of scalar products of vectors.

4. Vector or cross-product

• Vector or cross product of two vectors $\vec{A} \& \vec{B}$ written as $A \times B$
• $A \times B$ is a single vector whose magnitude is equal to the product of the magnitude of $\vec{A}$ \& $\vec{B}$ and the sine of the smaller angle $\Theta$ between them.
• $\vec{A} \times \vec{B}=A B \sin \Theta$

     The figure shows a representation of cross product of vectors.