What is the distance of the origin from the plane 2x + 6y - 3z + 7 = 0

1.	What is the distance of the origin from the plane 2x + 6y - 3z + 7 = 0?1. 12. 23. 34. 6
Answer» Correct Answer - Option 1 : 1 Concept: The distance of the origin (0, 0, 0) from the plane ax + by + cz + d = 0 is given by \(\rm \left\|\frac {(a)(0) +(b)(0) +(c)(0) + d }{\sqrt {a^2+b^2+c^2}}\right\|\) Calculation: We know that the distance of the origin (0, 0, 0) from the plane ax + by + cz + d = 0 is given by \(\rm \left\|\frac {(a)(0) +(b)(0) +(c)(0) + d }{\sqrt {a^2+b^2+c^2}}\right\|\) ⇒ The distance of the origin from the plane 2x + 6y - 3z + 7 = 0 \(=\rm \|\frac {(2)(0) +(6)(0) +(-3)(0) + 7 }{\sqrt {2^2+6^2+(-3)^2}}\|\) \(=\rm \|\frac { 7 }{\sqrt {49}}\|\) = 1 Hence, the distance of the origin from the plane 2x + 6y - 3z + 7 = 0 is 1.

What is the distance of the origin from the plane 2x + 6y - 3z + 7 = 0?1. 12. 23. 34. 6

Answer» Correct Answer - Option 1 : 1

Concept:

The distance of the origin (0, 0, 0) from the plane ax + by + cz + d = 0 is given by \(\rm \left|\frac {(a)(0) +(b)(0) +(c)(0) + d }{\sqrt {a^2+b^2+c^2}}\right|\)

Calculation:

We know that the distance of the origin (0, 0, 0) from the plane ax + by + cz + d = 0 is given by \(\rm \left|\frac {(a)(0) +(b)(0) +(c)(0) + d }{\sqrt {a^2+b^2+c^2}}\right|\)

⇒ The distance of the origin from the plane 2x + 6y - 3z + 7 = 0

\(=\rm |\frac {(2)(0) +(6)(0) +(-3)(0) + 7 }{\sqrt {2^2+6^2+(-3)^2}}|\)

\(=\rm |\frac { 7 }{\sqrt {49}}|\)

= 1

Hence, the distance of the origin from the plane 2x + 6y - 3z + 7 = 0 is 1.

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