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# NumPy | Vector Multiplication

• Last Updated : 05 May, 2020

Vector multiplication is of three types:

• Scalar Product
• Dot Product
• Cross Product
• Scalar Multiplication:
Scalar multiplication can be represented by multiplying a scalar quantity by all the elements in the vector matrix. Code: Python code explaining Scalar Multiplication

 `      ` `# importing libraries  ``import` `numpy as np``import` `matplotlib.pyplot as plt``import` `math`` ` `v ``=` `np.array([``4``, ``1``])``w ``=` `5` `*` `v``print``(``"w = "``, w)`` ` `# Plot w``origin ``=``[``0``], [``0``]``plt.grid()``plt.ticklabel_format(style ``=``'sci'``, axis ``=``'both'``, ``                     ``scilimits ``=``(``0``, ``0``))``plt.quiver(``*``origin, ``*``w, scale ``=` `10``)``plt.show()`

Output :

`w =  [20  5]` Dot Product multiplication: Code: Python code to explain Dot Product Multiplication

 `import` `numpy as np``import` `math`` ` `v ``=` `np.array([``2``, ``1``])``s ``=` `np.array([``3``, ``-``2``])``d ``=` `np.dot(v, s)``print``(d)`

Here, dot product can also be received using the ‘@’ operator.

d = v@s

Output :

`4`

Code: Python code explaining Cross Product

 `import` `numpy as np``import` `math`` ` `v ``=` `np.array([``4``, ``9``, ``12``])``s ``=` `np.array([``21``, ``32``, ``44``])``r ``=` `np.cross(v, s)``print``(r)`

Output:

`[ 12  76 -61]`

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