Direction ratios = cross product of normals: (2,1,1)×(3,−2,−1)=(1⋅(−1)−1⋅(−2),1⋅3−2⋅(−1),2⋅(−2)−1⋅3)=(1,5,−7).
The direction ratio's of line of intersection of two planes :
2x+y+z+47=0 and 3x−2y−z+41=0 are :
Held on 17 Aug 2022 · Verified 13 Jul 2026.
<1,5,−7>
<1,−1,4>
<2,1,1>
<3,−2,−1>
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The shortest distance between the following lines: $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$ $\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:
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