Find a.b when a = i + 2j – 3k, b = i + 2j – 3k, b= i+2j-k
Select one:
2
5
8
3
3
To find the dot product of two vectors a and b, we multiply the corresponding components of the two vectors and then add them up.
Given:
a = i + 2j – 3k
b = i + 2j – k
Let's calculate the dot product of a and b:
a.b = (i * i) + (2j * 2j) + (-3k * -k)
= i^2 + 4j^2 + 3k^2
= 1 + 4 + 3
= 8
Therefore, the value of a.b is 8.
To find the dot product (a·b) of two vectors a and b, you need to calculate the sum of the products of the corresponding components of the vectors.
Given a = i + 2j – 3k and b = i + 2j – k, we can calculate a·b as follows:
a·b = (i + 2j – 3k) · (i + 2j – k)
= i·i + 2j·i – 3k·i + i·2j + 2j·2j – 3k·2j – i·k – 2j·k + 3k·k
= 1 + 0 + 0 + 0 + 4 + 0 + 0 + 0 + 9
= 14
Therefore, the dot product of vectors a and b is 14. None of the given options (2, 5, 8, 3) matches the result.