Let the image of the point $(1,0,7)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ be the point $(\alpha, \beta, \gamma)$. Then which one of the following points lies on the line passing through $(\alpha, \beta, \gamma)$ and making angles $\frac{2 \pi}{3}$ and $\frac{3 \pi}{4}$ with $y$-axis and $z$-axis respectively and an acute angle with $x$-axis?

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YESPYQ · Accepted Answer

Correct answer: b) $(3,4,3-2 \sqrt{2})$. Given point P (1,0,7). Given line: $\frac{\left(x−1\right)}{1}=\frac{y}{\left(−3\right)}=\frac{\left(z−8\right)}{1}$ A point on line is A(1,0,8). Direction ratios of line = (1,−3,1). Find foot of perpendicular H from P to line. Using reflection formula: ${P}^{'}=2H−P$ After applying angle conditions given in question, required point obtained is the option corresponding to (B).

Let the image of the point \((1,0,7)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) be the point \((\alpha, \…

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