JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the plane \(x+3 y-2 z+6=0\) meet the co-ordinate axes at the points \(A, B, C\). If the orthocentre of the triangle \(ABC\) is \(\left(\alpha, \beta, \frac{6}{7}\right)\), then \(98(\alpha+\beta)^2\) is equal to \(........\).
- A \(280\)
- B \(281\)
- C \(282\)
- D \(288\)
Answer & Solution
Correct Answer
(D) \(288\)
Step-by-step Solution
Detailed explanation
\(A (-6,0,0) \quad B (0,-2,0) \quad C =(0,0,3)\) \(\overrightarrow{ AB }=6 \hat{ i }-2 \hat{ j }, \quad \overrightarrow{ BC }=2 \hat{ j }+3 \hat{ k }\), \(\overrightarrow{ AC }=6 \hat{ i }+3 \hat{ k }\) \(\overrightarrow{ AH } \cdot \overrightarrow{ BC }=0\)…
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