OnlineCBT
Physics · MOTION IN A PLANE
Englishतीन 3D सदिश \( \mathbf{A} = 3\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 4\hat{\mathbf{k}} \), \( \mathbf{B} = -\hat{\mathbf{i}} + 4\hat{\mathbf{j}} - 2\hat{\mathbf{k}} \), तथा \( \mathbf{C} = 2\hat{\mathbf{i}} + \hat{\mathbf{j}} - 5\hat{\mathbf{k}} \) दिए गए हैं। एक सदिश \( \mathbf{D} \) का परिमाण ज्ञात कीजिए ताकि \( \mathbf{A} + \mathbf{B} - \mathbf{C} + \mathbf{D} = \mathbf{0} \) हो।
सही उत्तर · विकल्प 3
\( 5\sqrt{2} \)
व्याख्या
\( \mathbf{D} = \mathbf{C} - \mathbf{A} - \mathbf{B} = (2 - 3 + 1)\hat{\mathbf{i}} + (1 + 2 - 4)\hat{\mathbf{j}} + (-5 - 4 + 2)\hat{\mathbf{k}} = 0\hat{\mathbf{i}} - \hat{\mathbf{j}} - 7\hat{\mathbf{k}} \). Magnitude \( |\mathbf{D}| = \sqrt{0^2 + (-1)^2 + (-7)^2} = \sqrt{50} = 5\sqrt{2} \).
