Multiplication Of Vectors MCQ - Practice Questions with Answers

1. If a vector is multiplied by any scalar

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

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

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

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

$$\text{ Vector }=-2\overrightarrow{A}$$
 

Scalar  or Dot or Inner Product

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

$\overrightarrow{A}\cdot \overrightarrow{B}=AB\cdot \cos \mathrm{\Theta }$

       Figure showing a representation of scalar products of vectors.

4. Vector or cross-product

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

     The figure shows a representation of cross product of vectors.