TS EAMCET · Maths · Three Dimensional Geometry
If \(\mathrm{M}\) is the foot of the perpendicular drawn from \(\mathrm{P}(1,2,-1)\) to the plane passing through the point \(A(3,-2,1)\) and perpendicular to the vector \(4 \hat{i}+7 \hat{j}-4 \hat{k}\), then the length of PM is
- A \(\frac{16}{3}\)
- B \(\frac{18}{5}\)
- C \(\frac{22}{9}\)
- D \(\frac{28}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{28}{9}\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through \(A(3,-2,1)\) and perpendicular to \(4 \hat{i}+7 \hat{j}-4 \hat{k}\) is \( \begin{aligned} & 4(x-3)+7(y+2)-4(z-1)=0 \\ & \Rightarrow 4 x+7 y-4 z+6=0 \end{aligned} \) Now,…
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