Answer: The value of a.b = 24.
Step-by-step explanation:
Since we have given that
[tex]\vec{a}=2\hat{i}+4\hat{j}\\\\and\\\\\vec{b}=(2\hat{i}+5\hat{j})[/tex]
We need to find the dot product of a.b:
As we know that
[tex]\hat{i}.\hat{i}=1\\\\and\\\\\hat{j}.\hat{j}=1[/tex]
So, it becomes,
[tex]\vec{a}.\vec{b}=(2\hat{i}+4\hat{j}).(2\hat{i}+5\hat{j})\\\\\vec{a}.\vec{b}=2\times 2+4\times 5\\\\\vec{a}.\vec{b}=4+20\\\\\vec{a}.\vec{b}=24[/tex]
Hence, the value of a.b = 24.
