OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीThree 3D vectors are given as \( \mathbf{A} = 3\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 4\hat{\mathbf{k}} \), \( \mathbf{B} = -\hat{\mathbf{i}} + 4\hat{\mathbf{j}} - 2\hat{\mathbf{k}} \), and \( \mathbf{C} = 2\hat{\mathbf{i}} + \hat{\mathbf{j}} - 5\hat{\mathbf{k}} \). Find the magnitude of a vector \( \mathbf{D} \) such that \( \mathbf{A} + \mathbf{B} - \mathbf{C} + \mathbf{D} = \mathbf{0} \).
Correct answer · Option 3
\( 5\sqrt{2} \)
Explanation
\( \mathbf{D} = \mathbf{C} - \mathbf{A} - \mathbf{B} = (2 - 3 + 1)\hat{\mathbf{i}} + (1 + 2 - 4)\hat{\mathbf{j}} + (-5 - 4 + 2)\hat{\mathbf{k}} = 0\hat{\mathbf{i}} - \hat{\mathbf{j}} - 7\hat{\mathbf{k}} \). Magnitude \( |\mathbf{D}| = \sqrt{0^2 + (-1)^2 + (-7)^2} = \sqrt{50} = 5\sqrt{2} \).
