JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the distance of the point \(P(43, \alpha, \beta), \beta<0\), from the line \(\vec{r}=4\hat{i}-\hat{k}+\mu(2\hat{i}+3\hat{k}), \mu\in R\) along a line with direction ratios \(3, -1, 0\) is \(13\sqrt{10}\), then \(\alpha^{2}+\beta^{2}\) is equal to ___ .
- A 170
- B 160
- C 180
- D 150
Answer & Solution
Correct Answer
(A) 170
Step-by-step Solution
Detailed explanation
\(\frac{x-43}{3}=\frac{y-\alpha}{-1}=\frac{z-\beta}{0} \Rightarrow P_1(43+3 \lambda, \alpha-\lambda, \beta)\) \(\frac{ x -4}{2}=\frac{ y }{0}=\frac{ z +1}{3} \Rightarrow P _1(2 \mu+4,0,3 \mu-1)\)…
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