JEE Main 2021 (Online) 31st August Morning Shift | 3D Geometry Question 87 | Mathematics

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

Let the equation of the plane, that passes through the point (1, 4, $$-$$3) and contains the line of intersection of the
planes 3x $$-$$ 2y + 4z $$-$$ 7 = 0
and x + 5y $$-$$ 2z + 9 = 0, be
$$\alpha$$x + $$\beta$$y + $$\gamma$$z + 3 = 0, then $$\alpha$$ + $$\beta$$ + $$\gamma$$ is equal to :

$$-$$23

$$-$$15

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-1

The equation of the plane passing through the line of intersection of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {2\widehat i + 3\widehat j - \widehat k} \right) + 4 = 0$$ and parallel to the x-axis is :

$$\overrightarrow r .\left( {\widehat j - 3\widehat k} \right) + 6 = 0$$

$$\overrightarrow r .\left( {\widehat i + 3\widehat k} \right) + 6 = 0$$

$$\overrightarrow r .\left( {\widehat i - 3\widehat k} \right) + 6 = 0$$

$$\overrightarrow r .\left( {\widehat j - 3\widehat k} \right) - 6 = 0$$

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

Equation of a plane at a distance $${2 \over {\sqrt {21} }}$$ from the origin, which contains the line of intersection of the planes x $$-$$ y $$-$$ z $$-$$ 1 = 0 and 2x + y $$-$$ 3z + 4 = 0, is :

$$3x - y - 5z + 2 = 0$$

$$3x - 4z + 3 = 0$$

$$ - x + 2y + 2z - 3 = 0$$

$$4x - y - 5z + 2 = 0$$

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + \widehat j + 4\widehat k} \right) = 16$$ and $$\overrightarrow r \,.\,\left( { - \widehat i + \widehat j + \widehat k} \right) = 6$$. Then which of the following points does NOT lie on P?

(3, 3, 2)

(6, $$-$$6, 2)

(4, 2, 2)

($$-$$8, 8, 6)

PREVIOUS NEXT