SATHEE: 3D Geometry 3 Question 38

3D Geometry 3 Question 38

38. The image of the line $\frac{x - 1}{3} = \frac{y - 3}{1} = \frac{z - 4}{- 5}$ in the plane $2 x - y + z + 3 = 0$ is the line

(a) $\frac{x + 3}{3} = \frac{y - 5}{1} = \frac{z - 2}{- 5}$

(b) $\frac{x + 3}{- 3} = \frac{y - 5}{- 1} = \frac{z + 2}{5}$

(d) $\frac{x - 3}{- 3} = \frac{y + 5}{- 1} = \frac{z - 2}{5}$

(2014 Main)

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Answer:

Correct Answer: 38. (d)

Solution:

Here, plane, line and its image are parallel to each other. So, find any point on the normal to the plane from which the image line will be passed and then find equation of image line.

Here, plane and line are parallel to each other.

Equation of normal to the plane through the point $(1, 3, 4)$ is

$\frac{x - 1}{2} = \frac{y - 3}{- 1} = \frac{z - 4}{1} = k [say]$

Any point in this normal is $(2 k + 1, - k + 3, 4 + k)$ .

Then, $\frac{2 k + 1 + 1}{2}, \frac{3 - k + 3}{2}, \frac{4 + k + 4}{2}$ lies on plane.

$\Rightarrow 2 (k + 1) - \frac{6 - k}{2} + \frac{8 + k}{2} + 3 = 0 \Rightarrow k = - 2$

Hence, point through which this image pass is

$(2 k + 1, 3 - k, 4 + k)$

i.e. $[2 (- 2) + 1, 3 + 2, 4 - 2] = (- 3, 5, 2)$

Hence, equation of image line is $\frac{x + 3}{3} = \frac{y - 5}{1} = \frac{z - 2}{- 5}$ .

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3D Geometry 3 Question 38

38. The image of the line $\frac{x - 1}{3} = \frac{y - 3}{1} = \frac{z - 4}{- 5}$ in the plane $2 x - y + z + 3 = 0$ is the line

Answer:

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चिकित्सा तैयारी

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3D Geometry 3 Question 38

38. The image of the line x−13=y−31=z−4−5 in the plane 2x−y+z+3=0 is the line

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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38. The image of the line $\frac{x - 1}{3} = \frac{y - 3}{1} = \frac{z - 4}{- 5}$ in the plane $2 x - y + z + 3 = 0$ is the line