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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 2

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 2

Answers (1)

Answer:

 Option(b)

Hint:

 Angle between two planes is 0.

Given:

 2x-y+z=6 \text { and } x+y+2z=3

Solution:

We know, the angle between two planes

a_1x+b_1y+c_1z+d_1=0 \text { and } a_2x+b_2y+c_2z+d_2=0 \text { is }

\theta =cos^{-1}\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1\, ^2+b_1\, ^2+c_1\, ^2}.\sqrt{a_2\, ^2+b_2\, ^2+c_2\, ^2}}

Here a1 = 2; b1 = -1; c1 = 1; d1 = -6 and a2 = 1; b2 = 1; c2 = 2; d2 = -3

So, the acute angle between the planes

2x-y+z=6 \text { and } x+y+2z=3 is

\begin{aligned} &\theta =cos^{-1}\frac{((2.1)+(-1.1)+(1.2))}{\sqrt{2^2+(-1)^2+1^2}.\sqrt{1^2+1^2+2^2}}\\ &=cos^{-1}\frac{(2-1+2)}{\sqrt{4+1+1}.\sqrt{1+1+4}}\\ &=cos^{-1}\frac{3}{\sqrt{6}.\sqrt{6}}\\ &=cos^{-1}\frac{3}{6}\\ &\theta =60^{o} \end{aligned}

Therefore, the acute angle between the planes

2x-y+z=6 \text { and } x+y+2z=3 \text { is } 60^o

Posted by

Gurleen Kaur

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