Question

Explain the multiplication of a vector by a real number.

Answer 1

Multiplication of vectors by a real number (scalar) is quite an easy concept.

in general form B = n . A  (which is different from scalar product of two vectors)

 

Now,

Let us say that we have a vector A and we want to multiply it by a real number, say 10. The resultant would be a vector B and would be written as

   B =  10 . A

If A = 5I -j +3k

then

 B = 10 . (5I -j +3k) 

or  B = 50i - 10j +30k

Answer 2

Answer:

When a vector is multiplied by a real number, the magnitude of the vector changes without a change in the direction of the vector.

Explanation:

Vector quantity is a physical quantity that has both magnitude and direction.

• For example a vector given by $\Vec A=5\hat i+4\hat j+3\hat k$
• The vector defines the respective magnitudes along the x, y and z directions.
• When a vector is multiplied by a real number or a scalar, the magnitude of the vector changes.
• But there will be no change in the direction of the vector.
• Let us multiply the above vector A by a real number, say 2.
• The resultant vector B would be

        $\vec B = 2\Vec A=2(5\hat i+4\hat j+3\hat k)=10\hat i+8\hat j+6\hat k$

• The magnitudes along the x, y and z directions are changed but the directions remain the same.

So, when a vector is multiplied by a real number, the magnitude of the vector changes without a change in the direction of the vector.