Question

Find magnitude of the vector \( \hat{i} + \hat{j} + \hat{k} \)

Hint:

The magnitude of a vector is found using the Pythagorean theorem in 3D space.

Answer 1

Step 1: Understanding the magnitude of a vector.
The magnitude of a vector \( \vec{v} = a\hat{i} + b\hat{j} + c\hat{k} \) is given by: \[ |\vec{v}| = \sqrt{a^2 + b^2 + c^2} \]

Step 2: Applying to the given vector.
For the vector \( \hat{i} + \hat{j} + \hat{k} \), the coefficients are \( a = 1, b = 1, c = 1 \), so: \[ |\hat{i} + \hat{j} + \hat{k}| = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3} \]

Step 2: Conclusion.
Thus, the magnitude of the vector \( \hat{i} + \hat{j} + \hat{k} \) is \( \sqrt{3} \).