JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(L\) be the line of intersection of planes \(\vec{r} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})=2\) and \(\vec{r} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})=2\). If \(\mathrm{P}(\alpha, \beta, \gamma)\) is the foot of perpendicular on \(L\) from the point \((1,2,0)\), then the value of \(35(\alpha+\beta+\gamma)\) is equal to :
- A \(134\)
- B \(119\)
- C \(143\)
- D \(101\)
Answer & Solution
Correct Answer
(B) \(119\)
Step-by-step Solution
Detailed explanation
\(P_{1}: x-y+2 z=2\) \(P_{2}=2 x+y-3=2\) Let line of Intersection of planes \(P_{1}\) and \(P_{2}\) cuts \(x y\) plane in point \(Q\). \(\Rightarrow \quad z\)-coordinate of point \(Q\) is zero \(\Rightarrow x-y=2\) and \(2 x+y=2\} \Rightarrow x=\frac{4}{3}, y=\frac{-2}{3}\)…
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