JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P\) be the plane passing through the points \((5,3\), \(0),(13,3,-2)\) and \((1,6,2)\). For \(\alpha \in N\), if the distances of the points \(A (3,4, \alpha)\) and \(B (2, \alpha\), a) from the plane \(P\) are \(2\) and \(3\) respectively, then the positive value of a is
- A \(6\)
- B \(4\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 8 & 0 & -2 \\ 4 & -3 & -2\end{array}\right|=\hat{ i }(-6)+8 \hat{ j }-24 \hat{ k }\) Normal of the plane \(=3 \hat{i}-4 \hat{j}+12 \hat{k}\) Plane: \(3 x-4 y+12 z=3\) Distance from \(A (3,4, \alpha)\)…
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