Question

DOT PRODUCT a . a = ? explain why, using a = [a1, a2, a3]

a) a1 * a2 * a3
b) a1 + a2 + a3
c) a1^2 + a2^2 + a3^2
d) a1 - a2 - a3

Answer 1

The dot product of vector a with itself is equal to the sum of the squares of its components, given by a1^2 + a2^2 + a3^2.

Step-by-step explanation:

The dot product of vector a with itself, denoted as a . a, can be calculated as the sum of the squares of its components. Therefore, the correct option is c) a1^2 + a2^2 + a3^2. Let's understand this with an example.

Suppose we have vector a = [2, -1, 3]. Then, the dot product a . a can be calculated as:

a . a = (2^2) + (-1^2) + (3^2) = 4 + 1 + 9 = 14

So, the dot product a . a is equal to 14.