Question

Find the magnitude of the vector \[ \left| \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \right|. \]

• A. 11
• B. \( \sqrt{11} \)
• C. \( \sqrt{7} \)
• D. \( \sqrt{10} \)

Hint:

To calculate the magnitude of a vector, square the coefficients of each unit vector, sum them up, and then take the square root.

Answer 1

The Correct Option is B

The given vector is \( \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \). The magnitude of a vector \( \mathbf{A} = a\mathbf{i} + b\mathbf{j} + c\mathbf{k} \) is given by: \[ |\mathbf{A}| = \sqrt{a^2 + b^2 + c^2}. \] For the vector \( \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \), we have \( a = 1 \), \( b = -1 \), and \( c = -3 \). Substituting these values into the formula for magnitude: \[ |\mathbf{A}| = \sqrt{1^2 + (-1)^2 + (-3)^2} = \sqrt{1 + 1 + 9} = \sqrt{11}. \] Thus, the correct answer is option (B) \( \sqrt{11} \).