Dot Product

Introduction to dot product:

The dot product is the multiplication of the two equal length sequences of numbers and one number can multiply the whole expression in the algebraic operation. This expression derived from the dot product and it often used to operation of the dot product. I like to share this Derivative of Dot Product with you all through my article.

For example: x , y is the given expression

The answer will be x ? y


Example problem for dot product:

Example 1:

Solve using dot product x = 3i + 5j and y = i + 2j

Solution:

Given that

x = 3i + 5j

y = i + 2j

Dot product    = x ? y

Take i terms and j terms multiply that separately

= (3) (1) + (5) (2)

= 3 + 10

= 13

The solution is = 13

Example 2:

Solve using dot product x = 8i + 7j and y = 9i + 4j

Solution:

Given that

x = 8i + 7j

y = 9i + 4j

Dot product    = x ? y

Take i terms and j terms multiply that separately

= (8) (9) + (7) (4)

= 72 + 28

= 100

The solution is = 100

Understanding Definition of Angle is always challenging for me but thanks to all math help websites to help me out.

Example problem for dot product:


Example 3:

Solve using dot product x = 6i + 4j and y = 3i + j

Solution:

Given that

x = 6i + 4j

y = 3i - j

Dot product    = x ? y

Take i terms and j terms multiply that separately

= (6) (3) + (4) (-1)

= 18 – 4

= 14

The solution is = 13

Example 4:

Solve using dot product x = 4i -7j and y = -3i - 2j

Solution:

Given that

x = 4i - 7j

y = -3i - 2j

Dot product    = x ? y

Take i terms and j terms multiply that separately

= (4) (-3) + (-7) (-2)

= -12 + 14

= 2

The solution is = 2

Example 5:

Solve using dot product x = -9i + 2j and y = 5i - 7j

Solution:

Given that

x = -9i + 2j

y = 5i - 7j

Dot product    = x ? y

Take i terms and j terms multiply that separately

= (-9) (5) + (2) (-7)

= (-45) + (-14)

= - 59

The solution is = -59