# NumPy | Vector Multiplication

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`
Cross Product: 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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