TS EAMCET · Maths · Three Dimensional Geometry
A plane \(\pi\) passing through the points \(2 \hat{i}-3 \hat{j}, 3 \hat{i}+4 \hat{k}\) is parallel to the vector \(2 \hat{i}+3 \hat{j}-4 \hat{k}\), If a line joining the points \(\hat{i}+2 \hat{j}\) and \(\hat{j}-2 \hat{k}\) intersects the plane \(\pi\) at the point \(a \hat{i}+b \hat{j}+c \hat{k}\), then \(a+b+2 c=\)
- A \(31\)
- B \(29\)
- C \(23\)
- D \(19\)
Answer & Solution
Correct Answer
(A) \(31\)
Step-by-step Solution
Detailed explanation
Equation of plane \(\pi\) is \(a(x-2)+b(y+3)+c z=0\) \((3,0,4)\) lies on this plane \(a+3 b+4 c=0\) ...(i) Normal to plane is perpendicular to \(2 \hat{i}+3 \hat{j}-4 \hat{k}\). \(2 a+3 b-4 c=0\) ...(ii) Solving (i) and (ii) we get \(a=-2 b, a=8 c, c=\frac{-b}{4}\) Equation of…
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