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Vector Addition
−
+
=
+
−
Given a = 3i 2j 7k and b 2i 4j 6k
+
ab = adding the components of the three
areas seperately
= (3 + 2)i + (2 – 4)j + (–7 + 6)k
+
ab = 5i – 2j – k
Vector Subtraction
Vector subtraction can be described as the addition of a vector with the negative of another vector. For example:
a = (3, 2) b = (2, 1)
a – b = a + (–b)
–b = –(2, 1) = –2, –1
a – b = (3, 2) + (–2, –1)
= (3 – 2) , (2 – 1) = (1, 1) = Unit Vector
Vector Multiplication
Before understanding vector multiplication, we need to understand that there are 2 different kinds of physical
quantities:
• Scalar: Scalar quantities are those physical quantities which contains only magnitude but no direction.
• Vector: These quantities have both magnitude as well as direction.
Vector multiplication is of two types: Dot product and cross product.
Vector Dot Product
Denoted by a,b, consider:
a = (1, 2, 3) b = (–4, 5, –1)
Multiply the respective areas
a.b = 1(–4) + 2(5) + 3(–1)
= –4 + 10 – 3 = 3 (Dot Product is a Scalar Value.)
Vector Cross Product
Denoted by a x b, consider:
a = (3, –3, 1) b = (–1, –4, 2) = (–3 × 2 –(–4 × 1) i –(3 × 2 –
i j k Representing −31 3 1 3 −3 (–1 × 1)j + (3 × –4) – (–3 × –1)k
a b= 3 − 3 1 the three axes in i −42 j − −12 + k −1 −4 = (–6 + 4)i – (6 + 1) j + (–12 –3)k
×
− 1 − 42 determinant form. = –2i – 7j – 15k
Cross Product is a vector value.
Brainy Fact
The goal of most ML projects is to create a model to perform certain functions, such as classifying text, predicting
house prices, or identifying emotions. In the deep learning model, this is achieved through a neural network,
where the layers of the neural network use matrix and vector multiplication to adjust parameters.
170 Touchpad Artificial Intelligence (Ver. 2.0)-XI

