JEE Mains · Maths · STD 12 - 10. vector algebra
A plane \(P\) is parallel to two lines whose direction ratios are \(-2,1,-3\), and \(-1,2,-2\) and it contains the point \((2,2,-2)\). Let \(P\) intersect the co-ordinate axes at the points \(A , B , C\) making the intercepts \(\alpha, \beta, \gamma\). If \(V\) is the volume of the tetrahedron \(OABC\), where \(O\) is the origin and \(p =\alpha+\beta+\gamma\), then the ordered pair \(( V , p )\) is equal to.
- A \((48,-13)\)
- B \((24,-13)\)
- C \((48,11)\)
- D \((24,-5)\)
Answer & Solution
Correct Answer
(B) \((24,-13)\)
Step-by-step Solution
Detailed explanation
Normal of plane \(P\) : \(=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\-2 & 1 & -3 \\-1 & 2 & -2\end{array}\right|=4 \hat{ i }-\hat{ j }-3 \hat{ k }\) Equation of plane \(P\) which passes through \((2,2,-2)\) is \(4 x-y-3 z-12=0\) Now, A \((3,0,0)\), B…
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