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CBSE Class 12 Math 2020 Delhi Set 3 Solved Paper

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Question : 3 of 11
Marks: +1, -0
The distance of the origin (0,0,0)(0,0,0) from the plane −2x+6y−3z=−7-2 x+6 y-3 z=-7 is :___
Solution:  
Concept:
The distance of the origin (0,0,0)(0,0,0) from the plane ax+by+cz+d=0a x+b y+c z+d=0 is given by ∣  (a)(0)+(b)(0)+(c)(0)+da2+b2+c2∣\left| \; \frac{(a)(0)+(b)(0)+(c)(0)+d}{\sqrt{a^2+b^2+c^2}} \right|
Calculation:
We know that the distance of the origin (0,0,0)(0,0,0) from the plane ax+by+cz+d=0a x+b y+c z+d=0 is given by ∣  (a)(0)+(b)(0)+(c)(0)+da2+b2+c2∣\left| \; \frac{(a)(0)+(b)(0)+(c)(0)+d}{\sqrt{a^2+b^2+c^2}} \right|
⇒\Rightarrow The distance of the origin from the plane 2x+6y−3z+7=02 x+6 y-3 z+7=0
=∣  (2)(0)+(6)(0)+(−3)(0)+722+62+(−3)2∣= \left| \; \frac{(2)(0)+(6)(0)+(-3)(0)+7}{\sqrt{2^2+6^2+(-3)^2}} \right|
=∣  749∣= \left| \; \frac{7}{\sqrt{49}} \right|
=1= 1
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