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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 11.3
(Question 25 - 28): In each of the following cases, determine the direction cosines of thenormal to the plane and the distance from the origin.
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Question : 28 of 78
Marks: +1, -0
2x+3yz=52x + 3y - z = 5
Solution:  
The given plane is 2x + 3y – z = 5 ...(1)
Direction ratios of the normal to the plane are < 2, 3, – 1 >.
∴ Direction cosines of the normal to the plane are :
24+9+1,34+9+1,14+9+1\langle \frac{2}{\sqrt{4+9+1}}, \frac{3}{\sqrt{4+9+1}}, \frac{-1}{\sqrt{4+9+1}} \ranglei.e., 214,314,114\langle \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{-1}{\sqrt{14}} \rangle
And distance of (1) from the origin =0+00514=514= \frac{\left|0+0-0-5\right|}{\sqrt{14}} = \frac{5}{\sqrt{14}}
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