Question

Find the magnitude of the vector: \[ \left| \hat{i} - \hat{j} - \hat{k} \right| \]

• A. 3
• B. 3
• C. 2
• D. 2

Hint:

To calculate the magnitude of a vector, square the coefficients of the unit vectors \( \hat{i}, \hat{j}, \hat{k} \), sum them up, and take the square root of the result.

Answer 1

The Correct Option is C

The magnitude of a vector \( \vec{A} = a\hat{i} + b\hat{j} + c\hat{k} \) is given by: \[ |\vec{A}| = \sqrt{a^2 + b^2 + c^2} \] For the vector \( \hat{i} - \hat{j} - \hat{k} \), we have \( a = 1 \), \( b = -1 \), and \( c = -1 \). So, the magnitude is: \[ |\hat{i} - \hat{j} - \hat{k}| = \sqrt{(1)^2 + (-1)^2 + (-1)^2} \] \[ = \sqrt{1 + 1 + 1} = \sqrt{3} \] Thus, the correct answer is: \[ \boxed{\sqrt{3}} \]