Question

The value of $\hat{i}\cdot\hat{i}+\hat{j}\cdot\hat{j}$ is

Hint:

The dot product of any unit vector with itself is always \(1\). Therefore \(\hat{i}\cdot\hat{i}=1\), \(\hat{j}\cdot\hat{j}=1\), and \(\hat{k}\cdot\hat{k}=1\).

Answer 1

Step 1: Recall the properties of unit vectors.
In vector algebra the standard unit vectors are \[ \hat{i},\hat{j},\hat{k} \] These vectors represent unit directions along the $x$, $y$, and $z$ axes respectively.

Step 2: Recall dot product rules.
The dot product of a unit vector with itself is \[ \hat{i}\cdot\hat{i}=1 \] \[ \hat{j}\cdot\hat{j}=1 \] because the magnitude of each unit vector is $1$.

Step 3: Add the two values.
\[ \hat{i}\cdot\hat{i}+\hat{j}\cdot\hat{j} \] \[ =1+1 \] \[ =2 \]
Step 4: Conclusion.
Thus the required value equals $2$.
Final Answer: $\boxed{2}$