TS EAMCET · Maths · Straight Lines
\(A(1,-2,1)\) and \(B(2,-1,2)\) are the end points of a line segment. If \(D(\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from \(C(1,2,3)\) to \(A B\), then \(\alpha^2+\beta^2+\gamma^2=\)
- A \(18\)
- B \(14\)
- C \(9\)
- D \(27\)
Answer & Solution
Correct Answer
(A) \(18\)
Step-by-step Solution
Detailed explanation
Equation of line \(A B\) is \(\begin{aligned} & \frac{x-1}{1}=\frac{y+2}{1}=\frac{z-1}{1}=K \\ & x=K+1 \Rightarrow \alpha=K+1 \\ & y=K-2 \Rightarrow \beta=K-2 \\ & z=K+1 \Rightarrow \gamma=K+1 \end{aligned}\) \(D R\) 's of line are \( \lt 1,1 ; 1\gt\) \(D R\) 's of…
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