SATHEE: 3D Geometry 3 Question 14

3D Geometry 3 Question 14

14. The equation of a plane containing the line of intersection of the planes $2 x - y - 4 = 0$ and $y + 2 z - 4 = 0$ and passing through the point $(1, 1, 0)$ is

(2019 Main, 8 April I)

(a) $x - 3 y - 2 z = - 2$

(b) $2 x - z = 2$

(d) $x + 3 y + z = 4$

Show Answer

Answer:

(c)

Solution:

Equations of given planes are

$and \begin{aligned} 2 x - y - 4 = 0 \\ y + 2 z - 4 = 0 \end{aligned}$

Now, equation of family of planes passes through the line of intersection of given planes (i) and (ii) is

$(2 x - y - 4) + λ (y + 2 z - 4) = 0$

According to the question,

Plane (iii) passes through the point $(1, 1, 0)$ , so

$\begin{array}{lc} (2 - 1 - 4) + λ (1 + 0 - 4) = 0 \\ \Rightarrow & - 3 - 3 λ = 0 \\ \Rightarrow & λ = - 1 \end{array}$

$\Rightarrow$

Now, equation of required plane can be obtained by putting $λ = - 1$ in the equation of plane (iii).

$\begin{array}{lrl} \Rightarrow & (2 x - y - 4) - 1 (y + 2 z - 4) & = 0 \\ \Rightarrow & 2 x - y - 4 - y - 2 z + 4 & = 0 \\ \Rightarrow & 2 x - 2 y - 2 z & = 0 \\ \Rightarrow & x - y - z & = 0 \end{array}$

पिछला

अगला

3D Geometry 3 Question 14

14. The equation of a plane containing the line of intersection of the planes $2 x - y - 4 = 0$ and $y + 2 z - 4 = 0$ and passing through the point $(1, 1, 0)$ is

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

3D Geometry 3 Question 14

14. The equation of a plane containing the line of intersection of the planes 2x−y−4=0 and y+2z−4=0 and passing through the point (1,1,0) is

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

14. The equation of a plane containing the line of intersection of the planes $2 x - y - 4 = 0$ and $y + 2 z - 4 = 0$ and passing through the point $(1, 1, 0)$ is