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Equation of a Plane Passing through a Point and Perpendicular to a Given Vector

Statement 1: ...

Question

Statement 1: A plane passes through the point A(2, 1, -3). If distance of this plane from origin is maximum, then its equation is $2 x + y - 3 z = 14$ .
Statement 2: If the plane passing through the point $A (\to a)$ is at maximum distance from origin, then normal to the plane is vector $\to a$ .

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

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Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

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Statement 1 is true and Statement 2 is false.

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Statement 1 is false and Statement 2 is true.

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Solution

The correct option is A Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
$A (2, 1, - 3)$
$2 x + y - 3 z = 14$
$\to$ A Should lie on the plane.
$2 (2) + 1 + (- 3) (- 3) = 14$
This is stated in statement 2.

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Similar questions

Statement 1:

(\sqrt{- 3 + 4 x - x^{2}} + 4)^{2} + (x - 5)^{2}

1 \leq x \leq 3)

36.

Statement 2:

(5, - 4)

(x - 2)^{2} + y^{2} = 1

6

(p \lor q) \land \sim p

\sim p \land q

M n^{2 +}, C r^{3 +}, V^{3 +}

T i^{3 +}

V^{3 +}

(8)^{\frac{1}{2}} B M

1

\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k

\to C =^i + 2^j +^k

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243

2

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

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