1

JEE Main 2021 (Online) 24th February Evening Shift

Numerical

+4

-1

Let $$\lambda$$ be an integer. If the shortest distance between the lines

x $$-$$ $$\lambda$$ = 2y $$-$$ 1 = $$-$$2z and x = y + 2$$\lambda$$ = z $$-$$ $$\lambda$$ is $${{\sqrt 7 } \over {2\sqrt 2 }}$$, then the value of | $$\lambda$$ | is _________.

x $$-$$ $$\lambda$$ = 2y $$-$$ 1 = $$-$$2z and x = y + 2$$\lambda$$ = z $$-$$ $$\lambda$$ is $${{\sqrt 7 } \over {2\sqrt 2 }}$$, then the value of | $$\lambda$$ | is _________.

Your input ____

2

JEE Main 2020 (Online) 4th September Morning Slot

Numerical

+4

-0

Out of Syllabus

If the equation of a plane P, passing through the intersection of the planes,

x + 4y - z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b $$ \in $$ R, then the distance of the point (3, 2, -1) from the plane P is...........

x + 4y - z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b $$ \in $$ R, then the distance of the point (3, 2, -1) from the plane P is...........

Your input ____

3

JEE Main 2020 (Online) 3rd September Evening Slot

Numerical

+4

-0

Out of Syllabus

Let a plane P contain two lines

$$\overrightarrow r = \widehat i + \lambda \left( {\widehat i + \widehat j} \right)$$, $$\lambda \in R$$ and

$$\overrightarrow r = - \widehat j + \mu \left( {\widehat j - \widehat k} \right)$$, $$\mu \in R$$

If Q($$\alpha $$, $$\beta $$, $$\gamma $$) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3($$\alpha $$ + $$\beta $$ + $$\gamma $$) equals _______.

$$\overrightarrow r = \widehat i + \lambda \left( {\widehat i + \widehat j} \right)$$, $$\lambda \in R$$ and

$$\overrightarrow r = - \widehat j + \mu \left( {\widehat j - \widehat k} \right)$$, $$\mu \in R$$

If Q($$\alpha $$, $$\beta $$, $$\gamma $$) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3($$\alpha $$ + $$\beta $$ + $$\gamma $$) equals _______.

Your input ____

4

JEE Main 2020 (Online) 9th January Evening Slot

Numerical

+4

-0

Out of Syllabus

If the distance between the plane,
23x – 10y – 2z + 48 = 0 and the plane

containing the lines $${{x + 1} \over 2} = {{y - 3} \over 4} = {{z + 1} \over 3}$$

and $${{x + 3} \over 2} = {{y + 2} \over 6} = {{z - 1} \over \lambda }\left( {\lambda \in R} \right)$$

is equal to $${k \over {\sqrt {633} }}$$, then k is equal to ______.

containing the lines $${{x + 1} \over 2} = {{y - 3} \over 4} = {{z + 1} \over 3}$$

and $${{x + 3} \over 2} = {{y + 2} \over 6} = {{z - 1} \over \lambda }\left( {\lambda \in R} \right)$$

is equal to $${k \over {\sqrt {633} }}$$, then k is equal to ______.

Your input ____

Questions Asked from 3D Geometry (Numerical)

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