Multiplication Of Vectors - Practice Questions & MCQ

UNIT VECTOR

A vector having magnitude of one unit is called unit vector. It is represented by a cap/hat over the letter. Eg- is called as unit vector of . Its direction is along the and magnitude is unit.

Unit vector along  -

ORTHOGONAL UNIT VECTORS

It is defined as the unit vectors described under the three-dimensional coordinate system along x, y, and z axis. The three unit vectors are denoted by i, j and k respectively.

Any vector (Let us say ) can be written as-

Where x, y and z are components of along x, y and z direction respectivly.

Magnitude of -

Unit vector-

1. If a vector is multiplied by any scalar

 (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 is multiplied by 2 then the direction of the resultant vector is the same as that of the given vector.

             

•  If is multiplied by (-2), then the direction of the resultant is opposite to that of the given vector.

               

3. Scalar  or Dot or Inner Product

• Scalar product of two vector & written as  

• is a scalar quantity given by the product of the magnitude of & and the cosine of a smaller angle between them.

       

     

       Figure showing the representation of scalar products of vectors.

Important results-

4. Vector or cross product

• Vector or cross product of two vectors   & written as

• is a single vector whose magnitude is equal to the product of the magnitude of & and the sine of the smaller angle   between them.

• 

   

     The figure shows the representation of the cross product of vectors.

Important results-